Most oats are cross-contaminated with wheat gluten.
If you'd like to try adding oats to a low gluten or gluten free diet, look for oats that state "Gluten Free" on the packaging, they can be found at most health food stores.
From the NIH: "In the past, people with celiac disease were advised not to eat oats. New evidence suggests that most people can safely eat small amounts of oats, as long as the oats are not contaminated with wheat gluten during processing. People with celiac disease should work closely with their health care team when deciding whether to include oats in their diet."
http://digestive.niddk.nih.gov/ddiseases/pubs/celiac/
Personally I think the jury is still out on whether or not oats are safe for those of us with celiac disease. Since there's a good chance that a minority of celiacs cannot tolerate oats, I'm going to wait several years before trying oats, if ever.