Heat the olive oil in a large pot over medium heat. Add the ground turkey and cook until it is browned and no longer pink, breaking it up with a spoon as it cooks.
Add the diced onion, red bell pepper, and minced garlic to the pot. Cook for 4 to 5 minutes until the vegetables soften.
Stir in the chili powder, cumin, oregano, salt, and black pepper. Cook for 1 minute to toast the spices.
Add the black beans, diced tomatoes with their juice, and chicken broth. Stir everything together and bring the soup to a simmer.
Reduce the heat to low, cover the pot, and let it cook for 20 minutes, stirring occasionally.
Ladle the soup into bowls and top each serving with chopped cilantro and a squeeze of lime.