In a large pot, heat oil over medium. Add onions, peppers and garlic. Cook, stirring, until softened slightly - about 5 minutes. Add chicken. Stir until no longer pink, about 3 minutes.
Add tomatoes, beans and seasonings. Stir. Bring to a boil, then reduce heat and cover. Simmer, stirring occasionally, for 15 minutes. Uncover and simmer, stirring occasionally, until thickened - about 10 more minutes.