In this paper, we investigate the relationship between behavioral characteristics derived from rich smartphone data and self-reported personality traits. Our data stems from smartphones of a set of 83 individuals collected over a continuous period of 8 months. From the analysis, we show that aggregated features obtained from smartphone usage data can be indicators of the Big-Five personality traits. Additionally, we develop an automatic method to infer the personality type of a user based on cellphone usage using supervised learning. We show that our method performs significantly above chance and up to 75.9% accuracy. To our knowledge, this constitutes the first study on the analysis and classification of personality traits using smartphone data.