There is a close race between the likes of 6-foot-6 small forward Chet Walker and Gilmore with the Bulls for who the best player from the 1970’s was for this franchise never to win MVP. It was a tooth and nail competition, but Walker was more consistent for the Bulls in his run with the team than Gilmore by a slight margin.
And Gilmore got an MVP award at one point when he played in the ABA. That has to count for something in terms of his personal accolades. But both Walker and Gilmore are Hall-of-Famers, and deservedly so. Both had accomplished basketball careers, and helped the Bulls reach the playoffs on multiple occasions.
During his six seasons with the Bulls, Walker was an All-Star selection four times. He was also an NBA Champion with the Philadelphia 76ers in 1966-67, and had seven All-Star selections in total over the course of his professional basketball career.
More than likely the best overall season for Walker with the Bulls came in 1971-71. Ironically enough that was the only season he had in the middle of his Bulls run that he wasn’t an All-Star selection. In 1971-72, Walker played in 78 games while averaging 22.0 points per game, 6.1 rebounds, and 2.3 assists, while shooting 50.5 percent from the field. That was good for a player efficiency rating of 21.8 and .268 win shares per 48 minutes.