New chuck for Rockwell drill press 11-280?

Sometimes, a hole can be drilled through the chuck towards the spindle and a punch inserted into it and when the chuck is supported on the vise jaws and the punch given a good whack with a hammer, the spindle will be knocked free of the chuck
There may already be a hole in the chuck. Can you tell by this photo?
chuck_inside.jpg
 
I now have the spindle with chuck out of the machine. Now what? I've been searching online videos but I'm not finding how to get this chuck off. Do I set it on a vise (chuck facing upward) with the spindle between the vise's jaws (loose, not clamped) and tap the body of the chuck on top of the vise's jaws?
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Johnny, you have undoubtedly found a way to separate the chuck from the spindle by now but on my drill press the quill and chuck were still on the machine. I used vice-grips to hold the pulleys and a pipe wrench to twist the chuck free. I did not know at the time that the chuck was mounted on a taper.
 
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