Heat oil in a large soup pot over medium heat. Add chicken and cook, stirring only occasionally, until brown, about 10 minutes. Sprinkle fajita seasoning over chicken and stir until well coated. Add bell peppers, poblano pepper, and onion; cook and stir over medium heat until vegetables are soft, about 10 minutes.

Pour in black beans, fire-roasted tomatoes, and chicken broth. Increase the heat to high and bring to a boil, then reduce the heat to medium-low and simmer for 30 minutes, stirring occasionally.

Season soup with hot sauce, salt, and pepper before serving.