In a large saucepan, add tomatillos and enough water to cover. Bring water to a boil and simmer until tomatillos are tender. Carefully remove tomatillos from the water and place in a bowl. Discard water.
In the same saucepan, add olive oil, onion, and garlic, and sauté until soft. Add onion and garlic to the bowl with the tomatillos.
Add half the tomatillo mixture, one can of green chilies, half the cilantro, and one cup chicken broth to a blender. Blend until smooth and add to the large saucepan. Repeat, and add remaining ingredients to the saucepan. Simmer 30 minutes, and add salt and pepper to taste.