Most likely the pulley is loose - worn inside the hole.
It is possible to drill/tap the front of the drive shaft to take a bolt. A member here sells/rents the tools to do this (Jerry, who posted the next message").
However, the hole in the pulley may be wallowed-out so badly that the balancer might wobble even with the bolt.
While the balancer is out, check the seal-surface (for the seal that sits in the cam/crank gears cover). If the seal surface on the balancers is grooved, a repair sleeve is available. If the seal looks bad, you might have to remove the cover to replace the seal. To do that, you will have to remove the oil pan. At that time, you might want to do a drill/tap to allow the cover to be removed by having the attachment bolts outside the front of the block (rather than from inside the pan)
Last edited by tclederman; 11/22/2016 4:10 PM. Reason: added note about Jerry