Traditionally made cheese is gluten-free. Cheese is made from milk, enzymes and bacteria, none of which contain gluten. The mold used in bleu cheese is sometimes grown on rye grains, but gluten has not been detected in dangerous amounts in bleu cheese made this way.
Gluten-containing ingredients may be added to cheese. This includes beer used in flavored cheeses and anti-clumping agents used in shredded cheese. Anti-clumping agents can be made from cellulose, which can be made from wheat. However, cheese manufacturers are required to include this on the label.
Gluten cross-contamination is possible in delis and bakeries. These locations may use flour, and that flour may contaminate any cheese they serve.