If your lathe came with a face plate, take it to your local HF store and see if it will thread on to the spindle on their lathe. If it does, order a replacement. There are also a number of on-line and e-bay dealers that sell chucks, but you often have to mount the chuck on a back plate, and if you are new to machining you probably shouldn't try it. Two places I've purchased from are: CDCO.com and the e-bay seller 800watts.
FWIW, these are not great lathes don't expect to work fast or take off a large cut of material when machining.
FWIW, these are not great lathes don't expect to work fast or take off a large cut of material when machining.