Chalmers began his career with Kirkintilloch Rob Roy FC in 1953, and spent time in England with Newmarket Town in England (1955-56) before returning to Scotland with Ashfield FC (1956-59). Later in 1959, however, the 23-year old signed with Celtic, where he would make his mark on history by scoring the winning goal in Celtic's 2-1 victory over Inter in the 1967 European Cup Final in Lisbon. The win made the Glasgow side the first British team to win the trophy and earned them the nickname "the Lisbon Lions."
He played 13 seasons for Celtic, claiming 6 league titles, 4 Scottish Cups, and 5 League Cups in addition to the European title.
Chalmers left Celtic in 1971 and played for Morton (1971-72) and Partick Thistle (1972-75) before retiring in 1975.