The U.S. Centers for Disease Control, a Department of Health and Human Services, has stated in their more recently updated information in regard to Chronic Fatigue Syndrome (CFS) that it can potentially coexist with hypothyroidism. More specifically, they state that symptoms of CFS and hypothyroidism are similar and that when low thyroid hormone has been treated sufficiently, a diagnosis of CFS may still be included if the chronic (severe and ongoing) fatigue and other symptoms persist.
http://www.bellaonline.com/articles/art61161.asp