In a large pot, heat butter or olive oil over medium heat. Add onion and cook until softened, about 5 minutes. Add jalapeno and garlic and cook for 1 minute more.
Add diced tomatoes, black beans, chicken broth, salt, and pepper. Bring to a boil, then reduce heat and simmer for 15 minutes.
Stir in cooked chicken and cilantro. Simmer for 5 more minutes.