Combine oil, juice from one lime, oregano, and black pepper in shallow, glass baking dish. Stir.
Place chicken breasts in baking dish and turn to coat each side. Cover dish and refrigerate overnight. Turn chicken periodically to marinate it on both sides.
Put water, tomatillos, and onion into saucepan. Bring to gentle boil and cook uncovered for 10 minutes or until tomatillos are tender.
In blender, place cooked onion, tomatillos, and any remaining water. Add garlic, jalapeño peppers, cilantro, salt, and juice of second lime. Blend until all ingredients are smooth. Place sauce in bowl and refrigerate.
Place chicken breasts on hot grill and cook until done. Place chicken on serving platter. Spoon tablespoon of lowfat sour cream over each chicken breast. Pour sauce over sour cream.
There are 445 calories in 1 serving of Grilled Chicken with Green Chili Sauce.