During his relatively short cycling career Valery Likhachov became a world, Olympic, and national champion. From 1969 to 1972 Likhachov was a multiple-time champion of the Soviet Union in road cycling and soon became part of the national team. He enjoyed international success almost immediately when the quartet of Likhachov, Valery Yardy, Boris Shukhov, and Viktor Sokolov won gold in the team time trial at the 1970 UCI Road World Championships in Leicester, England.
Two years later Likhachov won the overall classification at the Tour du Maroc, winning three individual stages along the way. He was then selected to compete at the München Olympics, where he, Yardy, Shukhov, and Gennady Komnatov won gold for the Soviet Union in the team time trial. Likhachov also placed 34th in the road race at the Games, finishing 2½ minutes behind the winner in the main peloton of riders. He continued to race for the next few years, winning stages at the Peace Race, the Tour of Algeria, and the Tour of Austria.