Celiac disease is a severe gluten allergy which limits the foods that a person can eat. The prime offender is wheat, which contains lots of gluten. However, many other foods which don't typically contain wheat still contain gluten in the form of a thickening agent. To be safe, a diet for celiac disease should only consist of fresh natural ingredients that don't contain wheat, such as fruits, vegetables, potatoes and rice, along with processed foods which are clearly marked as gluten free. Most packaged foods now come with a label that says gluten free or states that there is gluten, which means it should be avoided.