Preheat oven to 325 degrees.
Place chicken in a large saucepan; cover with water and cook over medium heat for 30 minutes. Remove from saucepan, set aside to cool then discard bones and skin and cut meat into cubes.
Heat the olive oil in a medium skillet over medium heat. Add onions; sauté for 5 minutes. Add garlic and tomatillos; simmer for 5 minutes. Add cilantro, green chilies, salt and pepper; transfer mixture to a blender or food processor and puree until smooth.
Lightly coat a 9- x 13-inch baking dish with olive oil. Layer ingredients in the following order: half of the tortillas, half of the sauce, half of the chicken then half of the cheese. Repeat process for a second layer, ending with cheese; bake, uncovered, for 1 hour.
Serve with sour cream and salsa.