Warm the olive oil in a large Dutch oven over medium heat. Add the ground turkey and cook until browned, breaking it into small pieces as it cooks.
Stir in the diced onion and bell pepper. Cook until softened, then add the minced garlic and cook for another minute.
Mix in the tomato paste, chili powder, cumin, smoked paprika, oregano, cayenne, salt, and black pepper, stirring until the spices become fragrant.
Add the diced sweet potatoes, black beans, kidney beans, diced tomatoes, and chicken broth. Stir everything together until well combined.
Bring the chili to a gentle boil, then reduce the heat and simmer uncovered until the sweet potatoes are tender and the chili has thickened.
Finish with the lime juice and stir well before serving. Ladle into bowls and add your favorite toppings.