Despite his unsavory past, Chase received a certain amount of National Baseball Hall of Fame support early in its history. During the inaugural Hall of Fame balloting of 1936, Chase garnered 11 votes and was named on 4.9% of the ballots. This total was more votes than 18 future Hall of Famers including such greats as Connie Mack, Rube Marquard, Mordecai "Three Finger" Brown, Charlie Gehringer, and John McGraw as well as the banned Shoeless Joe Jackson. In 1937, he received 18 votes (9%) which was more than 32 future Hall of Famers. Chase was dropped from the ballot following the 1937 vote. He never received the 75 percent support required for enshrinement, largely due to an informal agreement among the Hall of Fame voters that those deemed to have been banned from baseball should be ineligible for consideration.