Heat the olive oil in your large pot over medium heat. Add the diced onion and bell pepper, cooking until softened, about 5 minutes. Stir in the minced garlic and cook for another 30 seconds until fragrant.
Add the ground turkey to the pot, breaking it up with your spoon. Cook until no longer pink, about 6–8 minutes.
Sprinkle in the chili powder, cumin, paprika, salt, and pepper. Stir well to coat the turkey and vegetables evenly. Toast the spices briefly in the pot to unlock their full aroma.
Pour in the drained kidney beans, black beans, diced tomatoes with their juices, and chicken broth. Stir everything together, scraping any browned bits from the bottom of the pot.
Bring the chili to a gentle boil, then reduce the heat to low. Cover and let it simmer for 25–30 minutes, stirring occasionally.
Once the chili has thickened, stir in the lime juice. Taste and adjust seasoning if needed. Serve hot, garnished with chopped cilantro.