George "Chief" Armstrong spent his childhood in the small town of Falconbridge, near Sudbury, Ontario. He was born of Irish-Algonquin heritage and his father worked in the nickel mines of Sudbury while young George worked at improving his hockey skills at the local rink. The Toronto Maple Leafs put Armstrong on their protected list while he was playing with the Copper Cliff Jr. Redmen of the NOHA in 1946-47. The following season, when the Leafs Junior A affiliate in Stratford needed an additional player, Armstrong was assigned to go. He promptly led the league in scoring with 73 points in 36 games and won the most valuable player award. The Maple Leafs wasted no time in re-assigning him to their main junior affiliate, the Toronto Marlboros of the OHA, for the 1948-49 season.
Armstrong was moved up to the senior Marlies in time for the 1949 Allan Cup playdowns and stayed with the club on a full time basis for the 1949-50 season. He registered 64 goals in 45 games and a further 19 goals in 17 Allan Cup playdown games as the Marlboros captured the 1950 Canadian senior hockey championship. It was during the Allan Cup tournament that the Marlies visited the Stoney Indian Reserve in Alberta. When the band heard of Armstrong ancestral background they dubbed him Big Chief Shoot the Puck and presented him with a ceremonial headdress.
He played the majority of his first two pro seasons with the Leafs' AHL farm team in Pittsburgh before making the big club for good at the start of the 1952-53 season. Armstrong was never a great skater but was rarely out of position; he knew how to play the angles on the opposing forwards and was a great corner man in the offensive zone. He never attained the scoring heights in the NHL as he had in his junior and senior days but Armstrong brought determination, leadership, and humour to a Leafs squad that was trying to escape the shadow of the Barilko tragedy in the early 1950s.
Armstrong was named as captain of the Leafs to start the 1957-58 season and was called by Conn Smythe "the best captain, as a captain, the Leafs have ever had." Smythe later honoured his captain by naming one of his horses Big Chief Army, something Smythe had done on only two other occasions for Charlie Conacher and Jean Beliveau.
After his retirement, Armstrong coached the Toronto Marlboros to Memorial Cup victories in 1972-73 and 1974-75 before accepting a scouting position with the Quebec Nordiques in 1978. Armstrong was with the Nordiques for nine years before returning to Toronto as assistant general manager and scout in 1988. His first year back was an eventful one and Armstrong found himself in the uncomfortable role as interim replacement coach for the final 47 games of the 1988-89 season. By the next year he had returned to his preferred role as a scout for the organization, primarily covering the Ontario Hockey League in the Toronto area.
George Armstrong was inducted into the Hockey Hall of Fame in 1975.