Automatically detecting and analyzing personality traits can aid in several other applications in domains like mental health recognition and human resource management. The primary limitation of a wide range of techniques used for personality prediction so far is that they analyze these traits for each individual in isolation. In contrast, personality is intimately linked with our social behavior. In this work,we conduct an experiment where the subjects participated in peer-to-peer conversations in Hindi. To the best of our knowledge, no work has been done on analyzing personality in such a setting.Our contributions include the first peer-to-peer Hindi conversation-based dataset for personality prediction, Vyaktitv, which consists of high-quality audio and video recordings of the participants, along with Hinglish-based textual transcriptions for each conversation. The dataset also contains a rich set of socio-demographic features, including gender, age, income, and several others, for all the participants. We release the dataset for public use, along with a preliminary multimodal analysis of the Big Five personality traits based on audio, video, and linguistic features.