The helicopter was tied down overnight on the helideck of an offshore oil platform. The pilot stated the helicopter preflight had been completed hours prior to the first flight. During the walk-around prior to the first flight of the day, he overlooked the right rear tie-down which was one of four connected to the fuselage. The pilot attempted to takeoff with the tie-down still attached to the helicopter which resulted in a dynamic rollover. The helicopter remained on the helideck. Substantial damage resulted to the tailboom and the right side of the helicopter.