Zenker's Diverticulum which is also not very common.
Check out the barium swallow which shows a barbell like image. The "barbell" part is the abnormal pouch and is found on both sides.
A paper was actually written about this condition by Dr. Chang.
Bilateral Pharyngoceles (versus Branchial Cleft Anomalies?) and Endoscopic Surgical Considerations. Annals of Otology, Rhinology, & Laryngology. 114(7):529-532, 2005.