Place chicken breasts in a large pan, cover with the cold water and bring to as simmer. Simmer vey gently for 20 minutes, until chicken is cooked through. Remove chicken and cool slightly, reserving chicken broth.
Heat oil in a skillet. Add onion, garlic and saute until softened, about 10 min. Add green chiles, cumin, oregano, cloves, cayenne pepper and salt and pepper to taste; saute 2 minutes.
Add vegetable mixture to the pan with the chicken and the broth. Add beans and simmer 1 1/2 hours. Top each serving with Monterey Jack cheese.