Carl Zimmer at the Loom has a nice summary of recent progress understanding the genetic basis for human language. FoxP2, a gene which is mutated in people with specific language difficulties, has a homologue in mice and chimpanzees (although the human variant seems to have been under intense selective pressure). Mice lacking FoxP2 show deficiencies in their communication via squeaking, suggesting that the evolutionary toolkit necessary for the emergence of human language has been around for a long time. (The exact brain deficiency in these mice does not appear to match the deficiency in humans with language aphasias).
The second half of his post concerns a better understanding of Broca's area, the area thought to be responsible for human speech. Monkeys have a similar area, and stimulation of this brain region elicits mouth and tongue movements. Again, the raw materials which natural selection has acted upon in humans seems to have been in place for a while.