Chuck probably could
Don't put a new chassis under it unless you have no alternative. Anytime I run across anything old, I go down the checklist: is anything obviously loose? Are the wheels clean? Is there so much rust that something could be shorted? Is there zinc pest on anything important? (That would be the one circumstance in which I'd put a new chassis under it without debate.)
Gabe just suggested that you check the brushes and brush plates (and the springs if it has them.) If you have a voltmeter, it'll tell you whether or not the armature is any good. If not, that can be fixed too.
Based on our experiences with old tinplate, most of the time it's dusty or rusted. Clean it up and shake the rust loose (gently) and it'll probably go.
--Becky