In online social networks, users tend to select information that adhere to their system of beliefs and to form polarized groups of like minded people. Polarization as well as its effects on online social interactions have been extensively investigated. Still, the relation between group formation and personality traits remains unclear. A better understanding of the cognitive and psychological determinants of online social dynamics might help to design more efficient communication strategies and to challenge the digital misinformation threat. In this work, we focus on users commenting posts published by US Facebook pages supporting scientific and conspiracy-like narratives, and we classify the personality traits of those users according to their online behavior. We show that different and conflicting communities are populated by users showing similar psychological profiles, and that the dominant personality model is the same in both scientific and conspiracy echo chambers. Moreover, we observe that the permanence within echo chambers slightly shapes users' psychological profiles. Our results suggest that the presence of specific personality traits in individuals lead to their considerable involvement in supporting narratives inside virtual echo chambers.