By 1965, at age 16, Kuchinskaya was the USSR national champion. At the 1966 World Championships, after winning her second Nationals title, the USSR Cup and the World Trials, she established herself as one of the stars of the Soviet team, winning gold medals in three of the four event finals (balance beam, uneven bars and floor exercise), a bronze on vault, and silvers in the all-around and team events. Kuchinskaya continued her winning streak in 1967, when she won the pre-Olympic test event in Mexico City and swept the USSR Nationals, walking away with the all-around title and every single event final gold medal.