By some estimates, Chicago has the nation's third-largest population of Mexican immigrants (after Los Angeles and Houston). The origins of the community date back to 1910, when Mexicans began coming to Chicago to work in the city's meatpacking, steel, and railroad industries. The Maxwell Street Market is officially almost as old, having been recognized by the city in 1912—but it evolved out of an aggregation of Italian, Greek, Czech, Bohemian, and eastern European Jewish vendors' stands and pushcarts that first gathered along Maxwell Street in the 1870s. Two waves of migration from the South, in the 1920s and again in the 1940s, added an African-American presence. There may have been Mexican merchants on Maxwell Street 70 or 80 years ago—and by the 1970s, vendors from the nearby barrio of Pilsen were selling steaming-hot tamales, fruits, and vegetables there. Five years ago, Maxwell Street Market was run out of its historic home, largely to make way for an expanding University of Illinois at Chicago campus. It reopened a week later three blocks east on Canal Street as the New Maxwell Street Market, and today, Mexican merchants are in the majority.

I like to enter the market—open only on Sundays—near the southern end, at 14th Street, and go straight to one of the best produce stalls, which in the summer and fall features locally grown vegetables: tomatoes; tomatillos; shell beans; tan-skinned pumpkins for Mexican soups, stews, and sweets; purple-tinged, three-foot stalks of huanzontle, a wild green whose seed heads are poached, battered, and fried; and a rainbow of chiles. (The piles of mean-looking cactus paddles and spiny chayotes—cousins of the smooth chayotes now common in supermarkets across the country—come from Mexico.) Regina Quezada and her family, from Guerrero, have had this space for five years now. Though she can be polished and cordial, this lively marchanta—as produce vendors are often called in Mexico—can swing into loud, hard-nosed haggling at the bat of an eye, and then calmly continue stringing up decorative clusters of freshly dug jicamas, top-on beets, and bunches of serranos on the stem, ripened to the color of fire.

Across from Señora Regina's stall, the smell of a classic Mexican broth saturates the air with the gaminess of goat and ground chile. There, vendors are assembling tacos of fork-tender birria de chivo (braised goat), wrapping the meat in floppy corn tortillas with salsa, onions, and cilantro. It's the braising broth, though, the consome, that transports the crowd. At this very moment, all over Mexico, their compatriots are participating in the same early Sunday ritual of consome de birria—elixir to the Mexican soul.

The scene so throbs with life—as many as twenty thousand people pass through the market on an average Sunday—that the Sears Tower, even the Chicago River winding along the market's east side, seem distant, blurred into soft focus. Latin music, drifting from bootleg cassettes, are the market's sound track—with lyrics like ''¿Como va el mundo?'' (''How's the world going?''), ironically suitable background music for huddles of men all having the same conversation: how to stretch a dollar, how to get more hours at work. Shoppers circle and swoop, making their way past heaps of chiles; around racks of First Communion dresses and warm-up suits; past stacks of duct tape, boxes of hand-rolled cigars, and hundreds of baseball caps proclaiming regional affiliations from Aguascalientes to Zacatecas and from northside to southside Chicago. One guy always shows up with hand-hammered copper cauldrons from Michoacan for making carnitas (slow-cooked pork). Many of the nonfood vendors simply lay out garage-sale paraphernalia. Or tools—loads of tools, thrown out like Pick Up Stix. Middle-aged men sort through them while their sons eye free weights hawked by youths whose bare torsos advertise the efficacy of their wares.

Geno Bahena immigrated to Chicago by himself at 16 with the same kind of hope for success that propels today's vendors at Maxwell Street Market. Now, after 16 years in the restaurant business, he's realized that hope: He's launched his own place, Ixcapuzalco, named after his hometown in Guerrero. But he gave up something by leaving Mexico as a young adult: He gave up his initiation into becoming a guardian of his own culture, on its own turf.

Four years ago, Geno's mother, Clementina Flores, arrived to help with that part of his education—to engender in him the values of rural Mexico. They make an easygoing pair: Geno, whose name is short for Generoso (generous), loves food and loves sharing it. Señora Clementina has a buoyant personality and a sudden, easy laugh. The market has become her touchstone in Chicago for the values she holds dear, including those of the traditional kitchen and family dining table. From Señora Regina, she buys hojas de milpa (corn leaves) for making flat, quick-cooking tamales nejos—Guerrero-style soul food that dates back to pre-Columbian times. From others, she picks up tomatillos, serrano chiles, and pumpkin seeds for the traditional accompaniment to those tamales: mole verde, a luscious, earthy sauce that radiates the elegant artlessness of native American cooking.

Señora Clementina made both dishes for us one Sunday afternoon after we'd left the market. Moving quietly but with the swift assurance of the best traditional cooks, she toasted the pumpkin seeds, then blended them into a beautiful, smooth puree with the tomatillos and green chiles, black pepper, and aromatic herbs—hierbas de olor—here, a classic combination of thyme, marjoram, and Mexican bay leaves. A little bit of fresh lard, melted in her earthenware cazuela, received the puree with a spattery welcome. As she thinned the mole with chicken broth to a creamy, soupy consistency, the mixer beat fresh corn masa with broth and just enough cal (calcium hydroxide) to make the raw masa ''grab'' the tongue, as Señora Clementina put it. With practiced dexterity she spread the thick batter over half of each corn leaf and folded the other half over it, then laid the packages in her steamer. When the pile inside reached about two inches in depth, she covered the steamer and set it over the flame. After just 20 minutes, we ate food that was about as simple and soulful as it gets: a bowl of nutty, fragrant, pale green mole, scooped up with pieces of tamal that were like thick, steamed tortillas with the softness of a plump rice-flour noodle.

Señora Clementina is an expert at bringing Mexico alive in a Chicago kitchen. But many of the market's cooks, worries chef Dudley Nieto—a native of Puebla—have been away from Mexico so long that they've lost touch with its authentic flavors. Or perhaps, he offers, they see more profit in food that appeals to second- and third-generation Mexicans, or non-Mexicans. For five years, Dudley—who's planning to open a restaurant called Chapultepec in Chicago this summer—has taken cooking groups shopping at the market. ''Maxwell Street is exciting—like markets in Mexico,'' he says. ''I love the fact that here in Chicago I can buy fresh nanches [a tart, cherry-sized fruit], aged cheese from Michoacan, and huitlacoche [corn fungus] grown by a Mexican farmer in Indiana. But the prepared foods...they're not exactly like those I was raised on.''

My suspicion is that Dudley's comments have something to do with the fierce regionality of Mexican cooks—and the cooks at the market come from all over Mexico (as well as the United States, as Dudley points out). The Mexico City-style huaraches—sandal-shaped corn masa cakes, often stuffed with a puree of black beans, slathered with salsa, and showered with lots of aged cheese—sold in several places at the market are a case in point. When I bite into one, I'm ecstatically transported to a little restaurant near where I lived in Mexico's capital. They're virtually identical. For Dudley, they're overwrought, bordering on inauthentic.

One of the huarache stands also makes seviche from, of all things, lake perch—a fine-textured freshwater fish—and _that's _a stretch for me. I'm used to Veracruz-style seviche, made with meaty mackerel or kingfish. Though the market version is piled on crispy tostadas and crowned with avocado chunks the way seviche is served on the beaches in Mexico, it isn't as satisfying to me as the original, or even as satisfying as the same stall's octopus-and-shrimp cocktail or its heady, green chile-spiked seafood soup. On the other hand, one of my favorite street nibbles at the market is an empanada, a crisp fried turnover, filled with cinnamony rice pudding. And, well, I've never seen anything quite like it in the motherland; for one thing, it starts with a store-bought flour tortilla, an item not widely available in Mexico.

Many of the stalls don't have names, including my favorite, run by Gilberto Ramirez—a round-faced, fast-talking, hospitable man who beams when you compliment his food—and his wife, Maria Landa, who's quiet, neat, and has an easy, confident smile. Both are from Guerrero. Their stand is a large, tented affair with an army of cooks pressing out thick eight-inch corn tortillas on big round griddles. Their quesadillas, made with these fabulously fresh tortillas, are great. In addition to cheese, you can have them with stewed mushrooms or grilled steak, and a topknot of cilantro, lettuce, and tomatoes. The molcajetes, or stone mortars, on the counter hold one of the best table salsas in the market—made with tomatillos, garlic, lots of green chiles, and cilantro. The most distinctive dish here, though, is Señora Maria's zesty tomatillo sauce over tender braised tongue.

As I slide into a chair at a table in Señora Maria's stall, a plate of this delicacy in hand, a wiry fellow plops down across from me. Two days' worth of stubble sprouts on his face, and there's a lifetime of hard work in the creases of his hands. I sit for a moment staring at an improbable yet quintessentially Chicago sign across the way: TOMALES, NACHOS, PIZZA, HOT DOGS, PUPUSAS. Then I catch the man's eye. He immediately addresses me in Spanish. ''Good food here, huh? I came all the way from Madison, Wisconsin. You?'' ''I'm from here,'' I reply. I think of the stunning displays of organic fruits and vegetables, some of our country's best, at the Madison farmers' market, and say, ''That's some market you have in Madison.'' ''It's okay, I guess,'' he allows. ''A lot of cute food. But this is a market you can really eat from.'' Folding a handmade tortilla around shreds of chicken mole, he bites off a satisfying mouthful.