In a large pot, combine chicken pieces with enough broth to cover them completely. Bring to a gentle simmer over medium heat, cook for about 25-30 minutes until tender. Remove chicken, discard skin and bones, shred the meat.

In the same pot, add oil and sauté diced onions, sliced carrots, and chopped bell peppers for 5-7 minutes until softened.

Stir in rice, cumin, black pepper, and paprika. Cook for an additional 2-3 minutes, stirring constantly.

Return shredded chicken and reserved broth to the pot, bring to a boil, then reduce heat and simmer for 15-20 minutes.

Add frozen peas and chopped cilantro, stir, and cook for an additional 5 minutes. Squeeze lime juice into the soup before serving.