Robert Paradise began his interest in athletics, and hockey in particular, at the age of ten. He attended Cretin High School, where he starred in hockey, baseball, and football. From there, he moved on to St. Mary's College in Winona, Minnesota where he became an all-conference performer in the Minnesota Intercollegiate Athletic Conference for four consecutive years, (first as a center and then as a defenseman). It was at defense that the aggressive Paradise caught the eye of NHL scout and former Boston Bruins star, Fern Flaman. He passed up an opportunity to sign a Boston Red Sox contract in 1965 in order to complete his education.

After graduation from St. Mary's in 1966, Paradise joined the 1968 United States Olympic Team and later the 1969 National Team before turning professional with the Montreal Canadiens organization. After two years in the minors and a brief stint with the Minnesota North Stars, he was drafted by the Atlanta Flames in 1972 and then went on to a six plus years career with the Flames, Pittsburgh and Washington.

Paradise was a defensive-minded defenseman and at 6-1 and 205 pounds, was noted for his physical style of play. He received a Sports Illustrated recognition in 1976 when he checked Clarke Gilles, the New York Islanders tough-guy, in the play-off game between the Islanders and the Penguins.

Robert Paradise is the son-in-law of the Hall of Famer, Bob Dill.