Ding ding ding...
That is the truck backing up.
What operations are you trying to do?
The prime use of a drill chuck is to drill. One way or the other you will need one of those chucks at some point.
If on the other hand you have been planning to use the lathe then the drill chuck will be of very limited use as a drive center. If you are just doing pens you might get by but it will not work for larger operations.
If you have not done so yet please take advantage of the online resources or your own copy of Power Tool Woodworking for Everyone. Online version is at:
http://www.shopsmith.com/academy/welcome.htm
And read the section on lathe turning.
You then might take a look at the online catalog for the parts you want, or take your chances on ebay.
http://www.shopsmith.com/ownersite/index.htm
BTW good luck with your car restore.
Ed