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3 or 4 limes
2 bone-in, skin-on chicken breast halves, each about 10 oz.
1 tsp. kosher salt, plus more, to taste
1/2 tsp. freshly ground pepper, plus more, to taste
1 Tbs. extra-virgin olive oil
1 large white onion, chopped
5 garlic cloves, minced
1 jalapeño chili, seeded and minced
3 cups low-sodium chicken broth
3 cups water
1 1/2 tsp. Mexican oregano
1 Haas avocado, pitted, peeled and diced
2 oz. queso fresco or mild feta cheese, crumbled
Cut 1 lime into 4 to 6 wedges; set aside for serving. Juice as many of the remaining limes as needed to measure 1/4 cup.
Season the chicken breasts with the 1 tsp. salt and 1/2 tsp. pepper. In a large saucepan over medium heat, warm the olive oil. Add the chicken, skin side down, and cook until browned, about 5 minutes. Transfer the chicken to a plate. Add the onion to the pan and sauté until translucent, about 4 minutes. Add the garlic and chili and sauté until fragrant, about 1 minute. Add the broth, water, lime juice and oregano, then return the chicken to the pan.
Increase the heat to high and bring the liquid to a boil, skimming off any foam that rises to the surface. Reduce the heat to medium-low, cover partially and simmer until the chicken shows no sign of pink when pierced with the tip of a sharp knife near the bone, about 40 minutes.
Transfer the chicken to a carving board and let cool slightly. Meanwhile, keep the soup at a simmer. Remove and discard the skin and bones, and shred the chicken into bite-size pieces. Stir the chicken into the soup. Adjust the seasonings with salt and pepper.
Put the avocado, cheese and lime wedges in separate small bowls. Ladle the soup into warmed bowls and serve immediately. Pass the avocado, cheese and lime wedges alongside. Serves 4 to 6.