A number of lathe turning projects require that you turn a spindle without the benefit of a tailstock being in place to support the end. Things like tops, goblets and candleholders all require unsupported turning. Using cyanoacrylate (CA) glue, you can do this work even if you don't have a specialty chuck.
First, mount a faceplate and round dummy board on your lathe. Make concentric circles on the board so you can easily position your material in the center of the disc.