Rub chicken breasts on all sides with the zest of 1 lime, 1 teaspoon olive oil, 1 teaspoon salt, and 1/4 teaspoon black pepper.
Heat remaining oil in a large 4 1/2 quart pot over medium-high heat. Add chicken breasts and cook until browned on both sides, about 8 minutes (they won't be cooked through). Add onions, garlic, and jalapeños, and cook until starting to brown, about 2 minutes.
Add spices and remaining salt and cook, stirring until the spices are toasted and fragrant, about 1 minute more.
Add broth and bring to a boil. Reduce the heat to low, cover and simmer until chicken is cooked through, about 1 hour. Using tongs, remove chicken breasts to a plate. Using two forks, shred chicken into strips. Return to the pot.
Add beans, kale, and the juice of 3 limes and cook a few minutes to wilt the kale and warm the beans. Taste and add more lime juice or salt if needed.