Use a sharp knife to cut wonton wrappers diagonally in half to form 60 triangles. Spray a baking sheet with nonstick coating. Arrange one-third of the triangles in a single layer on prepared baking sheet.
In a small bowl stir together the olive oil, garlic, and basil. Brush the wonton triangles lightly with some of the oil mixture; sprinkle with some of the Parmesan or Romano cheese.
Bake in a 350 degree F oven about 8 minutes or until golden brown. Cool completely on a wire rack. Repeat with the remaining wonton triangles, oil mixture, and Parmesan or Romano cheese. Makes 60 chips (15 servings).