4 quarts chicken broth
Vegetable oil for deep-frying
3 corn tortillas, cut into strips 2 inches long
1 1/4 lb. boneless, skinless chicken breasts
3 Tbs. olive oil
1 large yellow onion, chopped
2 Tbs. minced garlic
2 to 3 tsp. finely minced jalapeño chili, with or without seeds, to taste
1 1/2 cups peeled, seeded and diced tomatoes (fresh or canned)
6 Tbs. chopped fresh cilantro
6 Tbs. fresh lime juice
1 1/2 tsp. salt, or to taste
1/2 tsp. freshly ground pepper
12 paper-thin lime slices, cut into quarters

In a large saucepan over high heat, bring 3 1/2 quarts of the broth to a boil. Reduce the heat so the broth boils gently and boil until reduced by half to about 7 cups, about 30 minutes.

Meanwhile, in a deep-fry pan, pour in vegetable oil to a depth of 2 inches and heat to 375°F on a deep-frying thermometer. Working in batches, drop in the tortilla strips and fry until golden and crisp, about 2 minutes. Using a slotted spoon, transfer the fried tortilla strips to paper towels to drain.

In a saucepan, combine the chicken breasts with the remaining 2 cups broth. Bring to a simmer and cook gently until the chicken is opaque throughout when cut with a knife, about 8 minutes. Transfer to a cutting board and, when cool enough to handle, cut the chicken breasts into bite-size pieces. Set aside. Discard the broth or reserve for another use. If not using immediately, cover and refrigerate.

In a large saucepan over medium heat, warm the olive oil. Add the onion and sauté, stirring occasionally, until tender and translucent, about 10 minutes. Add the garlic and jalapeño chili and cook for 1 to 2 minutes to soften. Add the reduced broth, increase the heat to high and bring to a boil. Reduce the heat to low, add the cooked chicken, tomatoes, cilantro, lime juice, salt and pepper, and simmer until the chicken is heated through, about 5 minutes. Taste and adjust the seasonings.

Ladle the soup into warmed bowls. Sprinkle the lime pieces and tortilla strips evenly over the tops. Serve immediately. Serves 6.