From Scientific American:
The left hemisphere of the human brain controls language, arguably our greatest mental attribute. It also controls the remarkable dexterity of the human right hand. The right hemisphere is dominant in the control of, among other things, our sense of how objects interrelate in space. Forty years ago the broad scientific consensus held that, in addition to language, right-handedness and the specialization of just one side of the brain for processing spatial relations occur in humans alone. Other animals, it was thought, have no hemispheric specializations of any kind.
Those beliefs fit well with the view that people have a special evolutionary status. Biologists and behavioral scientists generally agreed that right-handedness evolved in our hominid ancestors as they learned to build and use tools, about 2.5 million years ago. Right-handedness was also thought to underlie speech. Perhaps, as the story went, the left hemisphere simply added sign language to its repertoire of skilled manual actions and then converted it to speech. Or perhaps the left brain’s capacity for controlling manual action extended to controlling the vocal apparatus for speech. In either case, speech and language evolved from a relatively recent manual talent for toolmaking. The right hemisphere, meanwhile, was thought to have evolved by default into a center for processing spatial relations, after the left hemisphere became specialized for handedness.
More here.