The helicopter rolled over during an attempted takeoff. The student pilot reported that his instructor had just got out of the helicopter and he was going to fly his second supervised solo. The student said he was seated in the right-hand seat. He rolled the throttle up to 80 percent and let the engine governor bring the engine up to full operating power. The student then pulled in some collective and the helicopter got light on the skids. He felt the helicopter drift to the left and he countered with right cyclic. As he moved the cyclic right he felt the helicopter start to roll right. At that point he then put in full left cyclic, but the helicopter continued to roll over onto its right side. The student's flight instructor observed the event and stated that he saw the left skid come off the ground a little and the helicopter started to drift right. The helicopter then rolled very quickly on to its right side. The student pilot reported that the helicopter and engine had no mechanical failures or malfunctions during the flight.