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