Chimp males compete with each other regularly, but also come together to repair their relationships, de Waal said. This pattern of behavior is seen in human families and in the workplace -- these cycles of one-upmanship and reconciliation.

"There are many animals who are very good at cooperation, and I'm personally not convinced that we humans are necessarily best at that, but we are very good at it, that's for sure."

His next book, coming out this spring, is called "The Bonobo and the Atheist: In Search of Humanism Among the Primates," which brings together evidence that there are biological roots in human fairness and addresses the role of religion in society.