Blackman joined Chelsea at U13 level and progressed through the club's youth system. He made his first appearance in a senior match day squad on 29 October 2011, sitting on the bench for a Premier League match against Arsenal which Chelsea lost 3–5 at home. He began to train regularly with the first team squad in the 2011–12 season and was an ever-present as Chelsea U18 won that season's FA Youth Cup. In January 2012 he was also included on the club's Champions League A-list as a home-grown player, replacing Hilário and allowing Ryan Bertrand to be registered instead as the left-back did not meet the required number of years at the club to qualify as club-grown. This ensured that Blackman received a winner's medal after Chelsea defeated Bayern Munich in the 2012 UEFA Champions League Final. He also received a winner's medal for Chelsea's Europa League success the following season.