I don't keep the chains on mine, it wears out the bearings on the shielding. Just keep it greased and loose so if someone does come in contact with it the shielding can stop independent of the shaft.
I don't know if I ever shared this with you or if you've seen it in another thread but I had a Bushhog 306 that was much like yours until I made a few slight modifications. Those old mowers like you've got are as tough as nails!