Heat a large pot over medium heat; grease with cooking spray. Add chicken; cook and stir until browned, about 10 minutes. Stir in broth and cumin. Bring to a boil; reduce heat, cover, and simmer until flavors combine, about 20 minutes.
Stir salsa, lime juice, and cilantro into the pot; simmer until heated through, 5 to 10 minutes more.