Not all oats are created equal, and not all oats are gluten-free. The biggest problem when it comes to oats, or oatmeal, is contamination, which can happen in the field (if oats and wheat are grown side-by-side) or during processing (if the oats are processed on equipment that also processes wheat).
Look for oats with a certified gluten-free label, and beware of molasses- and brown sugar-flavored varieties, which can sometimes contain wheat-bearing caramel coloring.