I reckon chimps are crap at language because their working memory is too good.
The follow paper may perhaps be (mis)read and bent a bit to support my view :-)
Decaro, M. S. S., Thomas, R. D. D., and Beilock, S. L. L. (2007). Individual differences in category learning: Sometimes less working memory capacity is better than more. Cognition. To appear.
Data reported in Inoue, S. and Matsuzawa, T. (2007) [Working memory of numerals in chimpanzees. Current Biology, 17(23):R1004-R1005]. From the abstract:
Chimpanzee memory has been extensively studied  and . The general assumption is that, as with many other cognitive functions, it is inferior to that of humans ; some data, however, suggest that, in some circumstances, chimpanzee memory may indeed be superior to human memory . Here we report that young chimpanzees have an extraordinary working memory capability for numerical recollection—better even than that of human adults tested in the same apparatus following the same procedure.
Obvious problems with this comparison (e.g. amount of training required to do this and only this task; likely amount of training in the humans), but I’m always pleased to see “only humans can do x” type inferences falsified.