Subjects who have enrolled in the oculopharyngeal muscular dystrophy (OPMD) natural history study (Study BNTC-OPMD-NH-001) and have completed at least 6 months of follow up in Study BNTC-OPMD-NH-001 may be eligible to participate in this study, where all subjects will be treated with a single dose of BB-301. BB-301 will be injected directly into the middle pharyngeal constrictor muscle and the inferior pharyngeal constrictor muscle of the throat through the use of an open surgical procedure conducted under general anesthesia. The primary objectives of the study are to evaluate the safety of BB-301, to identify the best dose of BB-301 to administer to patients, and to characterize how well BB-301 works to improve the symptoms of dysphagia in patients with OPMD.