1. Warm oil in a large pot over medium heat. Add onion, bell pepper, jalapeño and garlic; sauté until tender, about 12 minutes. Transfer to a bowl. Add chicken to pot and cook, stirring, until no pink remains, about 8 minutes. Return vegetables to pot.
2. Add tomatoes, pumpkin, broth, chili powder, cumin and 1/2 tsp. salt. Bring to a boil. Reduce heat to medium-low and stir in all beans. Cover and simmer, stirring occasionally, until chili thickens slightly, about 30 minutes. Taste and season with salt and pepper.