Heat oil in a large pot over medium heat; sauté onion and bell pepper until softened, about 5 minutes.
Add garlic, chili powder, cumin, and smoked paprika; cook 1 minute until fragrant.
Stir in chicken pieces, coating with spices; pour in low-sodium broth, diced tomatoes, and black beans.
Bring to a simmer, cover, and cook 15–20 minutes until chicken is cooked through and flavors meld.
Shred chicken in the pot with two forks or leave whole; finish with lime juice and adjust seasoning.
Serve with avocado and a dollop of Greek yogurt.