In a large pot or dutch oven, heat the olive oil over medium heat. Add jalapeno, poblano and onion. Cook until soft - about 5 minutes.
Add garlic and spices. Cook 60 seconds and stir often.
Add the chicken stock (and water for thinner chili) and bring to a simmer. Add chicken and beans. Stir and cook until the chicken and beans heat through - about 5 to 10 minutes. Add salt, pepper and lime juice to taste.