Preheat oven to 325°F.
Grease shallow baking dish.
Cut 1/2 inch slice from top of each tomato; scoop out pulp and seeds, leaving 1/4 inch shell (reserve pulp for another use such as salads or sauces).
Invert tomatoes on paper towel-lined plate and let drain 20 minutes.
Combine 3 cups of the cheese, the chilies, oregano and garlic in medium-size bowl.
Divide mixture evenly among tomato shells.
Arrange tomato shells in prepared dish; bake 20 minutes.