Autism spectrum disorder (ASD) is a developmental disorder characterized by stereotypies or repetitive behaviors and impairments in social behavior and socio-communicative skills. One hallmark phenotype of ASD is poor joint attention skills compared to neurotypical controls. In addition, individuals with ASD have lower scores on several of the Big 5 personality dimensions, including Extraversion. Here, we examine these traits in a nonhuman primate model (chimpanzees; Pan troglodytes) to further understand the relationship between personality and joint attention skills, as well as the genetic and neural systems that contribute to these phenotypes. We used archival data including receptive joint attention (RJA) performance, personality based on caretaker ratings, and magnetic resonance images from 189 chimpanzees. We found that, like humans, chimpanzees who performed worse on the RJA task had lower Extraversion scores. We also found that joint attention skills and several personality dimensions, including Extraversion, were significantly heritable. There was also a borderline significant genetic correlation between RJA and Extraversion. A conjunction analysis examining gray matter volume showed that there were five main brain regions associated with both higher levels of Extraversion and social cognition. These regions included the right posterior middle and superior temporal gyrus, bilateral inferior frontal gyrus, left inferior frontal sulcus, and left superior frontal sulcus, all regions within the social brain network. Altogether, these findings provide further evidence that chimpanzees serve as an excellent model for understanding the mechanisms underlying social impairment related to ASD. Future research should further examine the relationship between social cognition, personality, genetics, and neuroanatomy and function in nonhuman primate models.