I think I might have said in another thread how disappointed I am with the low light performance of the 30D at high ISO even with a f2.8 lens.
As Odille said perhaps its the body not so much the lens ... BUT ... you are using f6.3 at the long end as the wide open apeture which isnt great ... I guess it depends on how much $$$ you want to part with ! You could look at upto $6000 for a 1D mark III which apparently has awesome high ISO performance (will let you know next week !) OR you could look at going between $1200 - $2500 for a 70 - 200 f2.8 L (or IS version) which is an INCREDIBLE lens with your nice wide open apeture !
For low light no flash moving subjects you need to have your shutter somewhere near 1/320th or above to catch the action without blur, depending on what the action is as I would assume the world chess championships isnt that fast moving

. Ideally you would look at 1/640th or above !