Add chopped onion and saute 5 minutes. Add diced chilies, minced garlic, oregano, cumin, and chili powder. Saute for 5 minutes. Add beans, chicken broth, chopped tomatillos and cilantro. It's important that the chicken broth contain little or no salt.
Salt inhibits the softening of the seed coat of beans.
Therefore, if you add salt too early the beans with never soften up. Add turkey breast and simmer until just cooked through, about 20 minutes. Transfer turkey to plate. Cover with foil and refrigerate. Add turkey, green onions and lime juice to chili.