Time-stable personality traits, such as impulsivity and its relationship with functional and structural brain alterations, have gained much attention in the recent literature. Evidence from functional neuroimaging data implies an association between impulsivity and cortical as well as subcortical areas of the reward system. Discounting future rewards during impulsive decisions can be related to activation in the orbitofrontal cortex and striatum. Cortical structural changes in prefrontal regions have been found for introspective impulsivity measures. The present study focuses on brain regions associated with delay discounting to investigate structural manifestations of trait impulsivity. To test this, seventy subjects underwent structural magnetic resonance imaging (MRI) followed by a behavioral delay discounting task outside of the scanner to measure impulsivity with questions like: “Would you like to have 3 immediately or 10 in 5 days?”. The amount of smaller-but-sooner decisions was calculated and used as a measure of behavioral impulsivity. Furthermore, we estimated subjects individual delay discounting parameter K reflecting the tendency to discount future rewards. Behaviorally, we found strong evidence in favor of a discounting utility model compared to a standard hyperbolic model of choice valuation. Neuronally, we focused on cortical and subcortical brain structure and investigated the association of behavioral impulsivity with delay discounting tendencies and gray matter volume. Voxel-based morphometric analyses showed positive correlations between delay discounting and gray matter volume in the striatum. Additional analyses using Freesurfer provided evidence for a positive correlation between delay discounting and gray matter volume of the caudate. Taken together, our study provides strong evidence for a structural manifestation of time-stable trait impulsivity in the human brain.