Final answer:
The Chosin Reservoir Campaign was a 77-day siege during the Korean War where Marines successfully broke through Chinese encirclement.
Step-by-step explanation:
The battle in which Marines were held in a 77-day siege was the Chosin Reservoir Campaign. This campaign was one of the most brutal fights during the Korean War, in which United Nations forces, primarily made up of U.S. Marines, were encircled by Chinese troops in the winter of 1950. Despite being heavily outnumbered and facing harsh weather conditions, the Marines managed to break through the Chinese encirclement, inflicting significant casualties on the Chinese forces while successfully conducting a fighting withdrawal.