Oats do not contain gluten. They contain a similar protein called avenin and research has shown that most people with coeliac disease can safely eat avenin.
The main problem with a lot of the oats and oat products that you find in the supermarket is that they are very often contaminated with gluten from wheat, rye or barley during processing (such as harvesting or milling). Therefore, oats that are NOT labelled as gluten free should always be avoided.
Many specialist manufacturers now produce gluten free oats.
If you have an ongoing symptoms or any concerns about including gluten free oats in your diet, please speak to your health professional.