Although many of the great apes prefer one or the other hand to perform delicate tasks, Humans are unusual in that righties greatly outnumber lefties. Left-handed people (I am one!) show elevated rates of learning disorders such as dyslexia; tend to perform better on tasks engaging the right hemisphere; and may even have different brain representations of abstract constructs like "kindness." So there has been a sense for some time that left-handedness is a marker for a grab bag of brain differences. Left-handedness is also at least partially heritable, with genetic contributions accounting for about 24% of the variance in handedness in the general population.
variation in the gene PCKS6 as associated with left-handedness in individuals with dyslexia. This gene encodes a proprotein convertase, a type of enzyme which clip many different important signaling molecules. Intriguingly, PCKS6 is known to process an important set of developmental signals known as nodal proteins, and mice lacking PCKS6 develop left-right abnormalities in numerous organ systems such as the lungs and intestines. So it is plausible that similar genes are important in the developing human brain to subtly affect numerous brain functions.
It's important to note that this gene variation was only associated with left-handedness in their subjects who had dyslexia. The same gene variation did not even show the same trend in the general population. Nevertheless, the numerous changes in brain function associated with left-handedness makes this type of gene a plausible candidate for the genetic portion of the difference.