Heat olive oil in Dutch oven or deep skillet over medium-high heat. Saute chopped onion, green bell pepper, red bell pepper, and garlic in hot oil until tender but not yet browned, 5 to 7 minutes.
Pour chicken broth over the vegetable mixture; season with chili powder, cumin, salt, and black pepper. Place a lid on the pot, reduce heat to medium-low, and simmer for 30 minutes.
Stir black beans, stewed tomatoes, and chicken meat together in a separate pot over medium-low heat; bring to a low simmer. Stir the vegetable-broth mixture into the black bean mixture. Bring again to a simmer and cook, adding water as needed to keep the mixture from becoming too dry, until the flavors blend, at least 30 minutes.