Heat a large pot over medium heat and add the chicken pieces. Cook until lightly browned on all sides, about 5 minutes, then remove the chicken to a plate.
Add the onion, red bell pepper, and garlic to the same pot. Cook until the vegetables soften, about 4 minutes.
Stir in the cumin, chili powder, and oregano. Cook for 1 minute until the spices smell fragrant.
Return the chicken to the pot. Add the chicken broth and diced tomatoes with their juice. Bring the mixture to a simmer.
Cover and cook for 15 minutes until the chicken is cooked through.
Stir in the black beans and lime juice. Simmer uncovered for 5 more minutes. Season with salt and black pepper.
Ladle the soup into bowls and top each serving with chopped cilantro. Serve with lime wedges on the side.