Heini Hemmi joined the Swiss national alpine skiing team in 1969 and made his top-10 World Cup début in January 1970, finishing fifth in the slalom at an event in Wengen. Through February 1972 he only placed in the top-10 in four more races, never better than fourth, and then did not reappear as a significant player on the international scene until 1975. In March of that year he finally achieved his first podium finish, second in the giant slalom, and was eventually selected to represent his nation in this event at the 1976 Winter Olympics. At the Games, poor runs by favorites [Ingemar Stenmark] of Sweden and [Gustavo Thoeni] of Italy allowed Hemmi and his compatriot [Ernst Good] to nab the gold and silver medals respectively. Hemmi and Good also competed in the slalom, but neither completed the event.
Hemmi proved to be more than a one-hit wonder by winning four World Cup events and securing an additional eight podium finishes at the World Cup over the remainder of his career, and in 1976/77 won the seasonal World Cup in giant slalom. His accomplishments earned him the title of Swiss Athlete of the Year in 1976. Hemmi retired from active competition in 1979 and founded a retail corporation in 1984 that sold sporting equipment, and he sold this business in 2007 for a substantial sum.