Hi Lee.
Most three jaw chucks that are bundled with the smaller lathes tend to be hit and miss, sometimes you get a good one… Other times, well you know about those.
To my mind, and I am quite prepared to be corrected by other members, you have a few choices to choose from.
1. You could buy a "brand" name chuck at something approaching the price of the lathe itself usually.
2. You could buy an independent four jaw chuck. These tend to be more useful as the four jaw will hold square stock too, and setting the work piece central is not as difficult as you might imagine.
3. If all you do is turn smaller stock you could invest in a ER 32 collect chuck and collets, but this can become a limiting factor if you want to turn something larger than the collets will hold.
4. You could try grinding the jaws parallel, but this usually results in a wasted few hours as the jaws may well be perfect at the diameter you ground them on but any other diameter will see them shift again, this is because the jaws of the chuck are usually just fine, it's the scroll which opens and closes the jaws where the issues lie.
Myself, I went with a 100mm four jaw independent and have to say that it is possible to get your work piece to within a gnats whisker of dead centre, more if you take the time.
I might add that it MAY be worth your while looking at fitting a slightly larger version of whichever chuck you go with as there are back plates available that will allow you to fit a 100 or 125mm chuck rather than the 80mm that they come with.
Just remember though that with a larger chuck there is more inertia and momentum, so it's wise to ramp the speed up slowly to save you the cost of replacement fuses and be a little more patient when waiting for the lathe to spin down from the higher speeds.
Regards.
Bill.