Chetverukhin began appearing at major international events in 1965 and won his first Soviet national title in the 1966–67 season. The following season, he repeated as the national champion and also took gold at the 1968 Winter Universiade in Innsbruck, ahead of Marián Filc of Czechoslovakia. He finished 5th at the 1968 European Championships in Västerås, Sweden; 9th at the 1968 Winter Olympics in Grenoble, France; and 9th at the 1968 World Championships in Geneva, Switzerland.