Keene represented England for nearly two decades in international team events, beginning with the 1966 Chess Olympiad in Havana at age 18. He followed with the next seven straight Olympiads: Lugano 1968, Siegen 1970, Skopje 1972, Nice 1974, Haifa 1976, Buenos Aires 1978, and La Valletta 1980. His individual performances at Lugano and Haifa merited bronze medals (although individual medals were not, in fact, awarded at Haifa) and he was undefeated in three Olympiads – these two and Siegen. His later performances, though, were less impressive, with just two draws from four games at Buenos Aires and losses in both his games at La Valletta.