In reply to BolderLicious:
The french use something referred to as "pof" it is a kind of soft resin that is very sticky - it leaves a really nasty residue on the rock that quickly turns to a polished hard sheen that is very hard to brush off.
Chalk isn't used because it is "sticky" which rather negates your post and all of the replies IMO. It is used in order to dry the hands which are inevitably a bit sweaty and therefore slippery.
To those who are advocating not using chalk at all I have to agree to an extent, certainly on many routes or problems (particularly on easy ones) it really isn't necessary and I find it really funny when people chalk up to do their juggy warm up traverses indoors however I must admit I find it helps on harder stuff.
To the OP surely the answer is to work on getting stronger fingers than finding was of making your hands more sticky or are you planning on becoming the next spiderman?