I was reading an article in National Geographic not too long ago about how there is a team of biologists in Novosibirsk, Siberia who has dedicated their research to discovering which genetic factors bring about domestication in wild animals. Ultimately, the project concerns the 'Nature versus Nurture' question. Their main focus: replicating the domestication of wolves into dogs using silver foxes as the vehicle.
The project originally began with biologist Dmitry Belyaev who chose to create his base group by going to local fur farms and taking foxes; by the 1960s the experiment was going better than anyone could have expected, and it is still the only domestication research lab devoted to foxes in the world. In a mere nine generations, Belyaev was able to breed a strand of foxes that actually strove to create bonds with humans, not just foxes who would respond to humans due to conditioning.
The experiment involves testing the new litters of kits for either amicable or aggressive reactions to humans, and then only keeping the most approachable for further breeding. Over time, they developed one line of foxes that was completely domesticated and another that was excessively aggressive. This provided a great way to test whether the 'domestication trait' is due to genetics or environment. By taking a kit from an aggressive mother and having it be raised by a tame mother, the nature/nurture question was answered: the kit was still aggressive as an adult. After this clarification, the team became determined to pinpoint the exact gene(s) that code for domestication.
It is hard to narrow it down to just one gene, but once they figure out which is/are responsible, scientists will hopefully be able to apply it humans in order to better understand how we moved from chimpanzee to 'domestic' human.