A native of Brattleboro, Vermont, he originally competed in the NIS in the Nordic combined, but later switched to cross country skiing. In 1974 he was the first American to win a medal in international competition, placing third in the European junior championships. He also was the first American to win an Olympic medal in Nordic skiing, winning the silver in the 30 km for the 1976 Olympics (he remains the only North American male to win an Olympic medal in this event). Koch also finished 6th in the 15 km event at those same Winter Olympics.
Stress caused by media presence, along with asthma, plagued Koch after his early successes. Considered the top American sportsman at the 1980 Winter Olympics, he performed poorly and finished far out of contention in all of his races.
Afterwards, he developed a new skiing technique that resembled ice skating on skis, now known as the freestyle cross-country skiing technique. In 1982 won the Cross-country skiing World Cup for cross-country. Koch would earn a bronze medal in the 30 km event at the 1982 FIS Nordic World Ski Championships becoming the first non-European to ever medal in a cross country skiing at the World Championships (Canada's Sara Renner would become the second when she earned a bronze medal in the individual sprint at the 2005 FIS Nordic World Ski Championships in Oberstdorf.). He also finished 3rd in the 1983 World Cup. The freestyle skiing technique has been used in Biathlon competitions since 1985, has been mandatory in Nordic Combined since 1985, and has been part of all cross country skiing competitions since 1982.