His dad was a Senator at the time. From the Washington Post:
Late in September 1970, Gen. William C. Westmoreland, the Army chief of staff, appeared at Fort Rucker, and Gore was assigned to cover his visit. The day he arrived, Westmoreland went on a training exercise. As he was about to climb into a helicopter, he noticed the name tag on the reporter's uniform. "Gore," he said. "Are you any relation to the senator from Tennessee?" "Yes, sir," the private replied...
... Despite his views on the war, Gore was not a rebel at Fort Rucker. The dutiful son was now for the most part the dutiful soldier. He won a "special troops" soldier of the month award, which came with a $25 savings bond, then the more exclusive Post Soldier of the Month award, with double the prize money. The winners were chosen for their knowledge of military subjects, leadership qualities, outstanding military bearing and courtesy. He was also selected at least three times as "supernumerary of the guard mount"--which meant having the sharpest-looking uniform and the shiniest boots. The reward for that was being excused from guard duty...
... Before shipping out for Vietnam, Gore made a round of farewell visits. He and Tipper went to Baltimore, where they met Bart Day and Bob Somerby, two of the beloved motley crew from Harvard. Somerby lived in a spare apartment near Johns Hopkins. Both men were now teachers, jobs they had taken to avoid the draft, Day turning to it only after a brief and unhappy stint with the Peace Corps in Chile. Somerby and Day were dressed casually. The Gores looked pressed and neat, as though they had just been to church. The contrast struck Day as a symbol of how their lives were diverging. Al seemed mature and directed. He and Tipper seemed to know where they were going. "It was," Day thought, "as if they're grown-ups and we're not."...
http://www.washingtonpost.com/ac2/wp-dyn?pagename=article&node=&contentId=A48066-1999Dec29¬Found=true