Old thread, I know, but it might help someone. Anyway, I hook my tow chains to the horizontal holes in the OEM hitch. I used to hook them into the vertical holes and I'd end up fighting to remove them.
I basically point the hooks toward the centerline of the truck and hook them in. To take them off, I rotate them like I'm unhooking them while simultaneously pressing on the safety clasp. I believe the holes in the horizontal part of the hitch are cut closer to the edge so they take smaller hooks better. I hope this made sense.