Harris was a member of the Chelsea side which won the FA Youth Cup in 1961 and made his senior club debut in February 1962 in a 1–0 win against Sheffield Wednesday. Within a year, he had established himself as a regular in the side, a position he would hold for the next eighteen years. He formed an important part of new Chelsea manager Tommy Docherty's youth-oriented re-building of the club after relegation from the First Division alongside the likes of Peter Bonetti, Peter Osgood and Bobby Tambling.