Answer:
Nope. Wheat, rye, and barley have proteins that collectively are called 'gluten' in the food industry and the medical profession. Oats do not contain the same proteins.
However, the jury is still out on whether oats may cause reactions in a higher percentage of people with sensitivity to gluten, such as those with Celiac Disease. Also, oats, if grown with glutenous grains such as wheat, are considered to contain gluten due to the high risk of cross contamination.
[Oats grown isolated from glutenous grains are considered to be gf. An example of gluten free oats, grown in a dedicated environment, is McCann's Irish Oats.]
Correction: Gluten is 2 protiens that join, gliadin and glutelin. These protiens exist inside the plants cell ular structure and cannot cross contaminate by being grown "near" to wheat or some other gluten containing grain. Wheat has both proteins, oats only have one protein.
Cross contamination occurs when the different grains are processed in the same mill. Leftover wheat or rye is not cleaned away from the equipment, and the new incoming oats pick up the wheat or rye by-products.
Cross contamination is actual wheat or rye getting into the oats.
Certified gluten free oats are milled in a mill that exclusively does oats. (or corn)