In a large skillet over medium-high heat, heat oil. Add onion and pepper and cook until beginning to soften, about 4 minutes. Add ground turkey and cook, stirring occasionally, until turkey is golden (it doesn't have to be completely cooked through at this point). Season with salt and pepper, then stir in garlic and tomato paste and cook until fragrant, about 2 minutes. Transfer mixture to a slow cooker.

Once in the slow cooker, add tomatoes, black beans, kidney beans, chicken broth, chili powder, cumin and oregano. Cook on high for 4 hours, until chili has thickened. Check for seasoning and season with salt and pepper to taste.