Heat olive oil and butter in a large pot over medium-high heat. Place chicken in the pot. Cook and stir until chicken is no longer pink, 7 to 10 minutes.
Stir in carrot, onion, celery, garlic, chili powder, cumin, paprika, salt, and pepper. Cook and stir until onion is translucent and carrots begin to soften, 3 to 4 more minutes.
Stir in hot sauce, tomato sauce, crushed tomatoes, and white and red kidney beans. Bring to a boil, then simmer over medium-low heat until vegetables are tender and flavors have blended, about 1 hour.
