A centrifugal chuck for a surgical handpiece is adapted to automatically engage a surgical instrument so it may be driven by the handpiece. The centrifugal chuck comprises a pivotable trunnion body situated within a hollow drive shaft, the trunnion body having a throughbore coaxially aligned with the axis of the hollow drive shaft in order to receive the shaft of the surgical instrument. The trunnion body is secured to a pair of lever arms symmetrically situated about the exterior of the drive shaft, the lever arms extending in opposite proximal and distal directions from the pivotable attachment of the trunnion body to the drive shaft. Rotation of the drive shaft causes radially outward movement of the lever arms thereby misaligning the throughbore of the trunnion body relative to the drive shaft in order to frictionally engage the shaft of the surgical instrument. A spring member integrally formed with each lever arm maintains a predetermined bias on the trunnion body in order to provide a predetermined minimum amount of friction to enable the instrument shaft to be retained within the handpiece at speeds below those at which the centrifugal forces become operative. The invention also resides in the method of attaching a surgical instrument to a handpiece utilizing a centrifugal clutch.