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.

nutrition information (per serving):

Calories (kcal): 320; Fat (kcal): 12; Fat Calories (g): 100; Saturated Fat (g): 4; Protein (g): 29; Monounsaturated Fat (g): 4; Carbohydrates (g): 27; Polyunsaturated Fat (g): 3; Sodium (mg): 680; Cholesterol (mg): 65; Fiber (g): 4;