This study investigated the neural basis of individual variation in emotion regulation, specifically the ability to reappraise negative stimuli so as to down-regulate negative affect. Brain functions in young adults were measured with functional Magnetic Resonance Imaging during three conditions: (i) attending to neutral pictures; (ii) attending to negative pictures and (iii) reappraising negative pictures. Resting-state functional connectivity was measured with amygdala and dorsolateral prefrontal cortical (DLPFC) seed regions frequently associated with emotion regulation. Participants reported more negative affect after attending to negative than neutral pictures, and less negative affect following reappraisal. Both attending to negative vs neutral pictures and reappraising vs attending to negative pictures yielded widespread activations that were significantly right-lateralized for attending to negative pictures and left-lateralized for reappraising negative pictures. Across participants, more successful reappraisal correlated with less trait anxiety and more positive daily emotion, greater activation in medial and lateral prefrontal regions, and lesser resting-state functional connectivity between (a) right amygdala and both medial prefrontal and posterior cingulate cortices, and (b) bilateral DLPFC and posterior visual cortices. The ability to regulate emotion, a source of resilience or of risk for distress, appears to vary in relation to differences in intrinsic functional brain architecture.