Elizabeth Lonsdorf studied 17 chimps at Gombe National Park in Tanzania:
She and colleague William Hopkins noted which hand mothers and offspring used and found most of the chimpanzees showed a clear preference for one hand or the other, with the majority being left-handed.
Furthermore, they determined the handedness trait runs in families, with females tending to produce offspring with the same hand preference.
They also note that:
"...wild chimpanzees are usually left-handed and pass that preference to their offspring, while chimps in captivity are usually right-handed."
The above is a picture of a chimp in a zoo - note it is holding a tube in it's left hand and using a tool to fish out treats in it's right hand.
The above picture is of a chimp in the wild, unfortunately, it is using a tool in it's right hand as well. One picture, I hasten to add, does not invalidate the theory. At any rate, this suggests that the beginnings of brain lateralization was present before the split between humans and chimpanzees and occured at least five million years ago. One of the interesting aspects to come from the Study is that:
Another interesting aspect of the new research is that it demonstrates chimpanzees learning by imitation. The adult females studied each had quite distinct patterns of using short, medium and long fishing tools to varying degrees. The lengths of tool used by daughters greatly resembled their mothers’ choices, whereas the sons’ did not. “Obviously they are paying attention to their mother’s technique, while the sons are not,”
Here is a link to some interesting, short, movies of chimps:
Images of Life on Earth