Personality describes persistent human behavioral responses to broad classes of environmental stimuli. Investigating how personality traits are reflected in the brain's functional architecture is challenging, in part due to the difficulty of designing appropriate task probes. Resting-state functional connectivity (RSFC) can detect intrinsic activation patterns without relying on any specific task. Here we use RSFC to investigate the neural correlates of the five-factor personality domains. Based on seed regions placed within two cognitive and affective 'hubs' in the brain--the anterior cingulate and precuneus--each domain of personality predicted RSFC with a unique pattern of brain regions. These patterns corresponded with functional subdivisions responsible for cognitive and affective processing such as motivation, empathy and future-oriented thinking. Neuroticism and Extraversion, the two most widely studied of the five constructs, predicted connectivity between seed regions and the dorsomedial prefrontal cortex and lateral paralimbic regions, respectively. These areas are associated with emotional regulation, self-evaluation and reward, consistent with the trait qualities. Personality traits were mostly associated with functional connections that were inconsistently present across participants. This suggests that although a fundamental, core functional architecture is preserved across individuals, variable connections outside of that core encompass the inter-individual differences in personality that motivate diverse responses.