A tool holding apparatus adapted to releasably lock a tool, such as a drill or reamer, within the tailstock spindle of a lathe or the like to thereby prevent relative rotation between the tool and spindle. The holding apparatus comprises a supporting arm adapted to be clamped about the spindle, a mounting arm adapted to be secured to the tool, and an interconnecting rod which permits the supporting arm and mounting arm to freely move relative to each other in parallel planes such that the mounting arm becomes automatically centered about the axis of the tool.