Personality is known to be relatively stable throughout adulthood. Nevertheless, it has been shown that major life events with high personal significance, including experiences engendered by psychedelic drugs, can have an enduring impact on some core facets of personality. In the present, balanced-order, placebo-controlled study, we investigated biological predictors of post-lysergic acid diethylamide (LSD) changes in personality. Nineteen healthy adults underwent resting state functional MRI scans under LSD (75µg, I.V.) and placebo (saline I.V.). The Revised NEO Personality Inventory (NEO-PI-R) was completed at screening and 2 weeks after LSD/placebo. Scanning sessions consisted of three 7.5-min eyes-closed resting-state scans, one of which involved music listening. A standardized preprocessing pipeline was used to extract measures of sample entropy, which characterizes the predictability of an fMRI time-series. Mixed-effects models were used to evaluate drug-induced shifts in brain entropy and their relationship with the observed increases in the personality trait openness at the 2-week follow-up. Overall, LSD had a pronounced global effect on brain entropy, increasing it in both sensory and hierarchically higher networks across multiple time scales. These shifts predicted enduring increases in trait openness. Moreover, the predictive power of the entropy increases was greatest for the music-listening scans and when “ego-dissolution” was reported during the acute experience. These results shed new light on how LSD-induced shifts in brain dynamics and concomitant subjective experience can be predictive of lasting changes in personality.