Chicken Soup with Lime and Hominy

12 oz. boneless, skinless chicken breasts 1 Tbs. vegetable oil 1 small white onion (8 oz.), chopped 4 medium cloves garlic, minced 1 small jalapeño, minced 1 quart lower-salt chicken broth 1 15-oz. can hominy, drained 1 tsp. dried Mexican oregano, crumbled if the leaves are large 4 to 5 Tbs. fresh lime juice Kosher salt and ground black pepper 2-1/2 oz. cotija cheese, cut into 1/4-inch cubes (1/2 cup) ________________________________________

Cut each chicken breast crosswise into 1-1/2-inch-wide pieces. Heat the oil in a 6-quart pot over medium-high heat until shimmering. Add the onion and cook, stirring often, until softened, about 5 minutes. Stir in the garlic and jalapeño and cook, stirring often, until fragrant, about 45 seconds. Add the broth, hominy, oregano, and chicken. Raise the heat to high and bring to a boil. Reduce the heat to medium, cover, and simmer gently, stirring occasionally and adjusting the heat as needed to maintain a simmer, until the chicken is cooked through, about 10 minutes. Transfer the chicken to a plate. Using two forks, shred the meat into bite-size pieces and return to the pan. Bring the soup back to a simmer over medium heat, stir in the lime juice, and season to taste with salt and pepper. Ladle into bowls, top with the cheese, and serve immediately.