Born in Big River, Saskatchewan, Neilson was a mix of Danish and Cree and grew up in an orphanage where he was educated and played hockey. He excelled for three years with the Prince Albert Mintos of the SJHL where he registered consecutive 20-goal seasons in 1960 and 1961. The New York Rangers prospect enjoyed a solid first pro season in the EPHL with the Kitchener-Waterloo Beavers in 1961-62.

Neilson looked solid as a rookie paired with Doug Harvey in 1962-63 and became a fixture on the New York defence for a dozen seasons. In 1967-68 he played superior defence and scored 35 points, which earned him selection to the NHL second all-star team. "Chief" scored a career-high ten goals and 44 points the next year then helped the Blueshirts become one of the league's elite clubs. In 1968-69, he was paired with rookie Brad Park and was credited with making a huge difference in the youngster's game.

The only down side for Neilson during this period was a serious knee injury in February 1970, which prevented him from making sharp turns the rest of his career. Beginning in 1970-71 the Rangers recorded three straight 100-point seasons and reached the Stanley Cup finals in 1972. They also reached the semi-finals in 1973 before rebuilding in mid-decade.

In June 1974, the Rangers left the veteran blueliner unprotected at the Intra-League Draft. Neilson was claimed by the weak California Golden Seals and he became a stabilizing influence on the club playing mostly with youngster Rick Hampton. He played two years on the West Coast and remained with the franchise during its two-year stay in Cleveland. Neilson retired in 1979 after playing a year in the WHA with Wayne Gretzky and the Edmonton Oilers. By this time chronic back problems had taken their toll and Neilson was not interested in the required surgery and rehabilitation at his age.