O'Neill signed for Celtic in 1959, aged 18, and made his debut in the 1961 Scottish Cup Final replay against Dunfermline. Although O'Neill did not play in Celtic's victory in the 1967 European Cup Final, he was an important member of the first team squad, making 32 appearances in the 1966–67 season. Many of those came during the first few months of the campaign (including the 1966 Scottish League Cup Final) as Jim Craig had temporarily dropped out of the team due to his dentistry studies.