Psychedelics are serotonergic drugs that profoundly alter consciousness, yet their neural mechanisms are not fully understood. A popular theory, RElaxed Beliefs Under pSychedelics (REBUS), posits that psychedelics flatten the hierarchy of information flow in the brain. Here, we investigate hierarchy based on the imbalance between sending and receiving brain signals, as determined by directed functional connectivity. We measure properties of directed functional hierarchy in a magnetoencephalography (MEG) dataset of 16 healthy human participants who were administered a psychedelic dose (75 micrograms, intravenous) of lysergic acid diethylamide (LSD) under four different conditions: eyes-closed with or without music and eyes-open with or without a video stimulus. Across the whole brain, LSD diminishes the asymmetry of directed connectivity when averaged across time. Additionally, we demonstrate that machine learning classifiers distinguish between LSD and placebo more accurately when trained on one of our hierarchy metrics than when trained on traditional measures of functional connectivity. Taken together, these results indicate that LSD weakens the hierarchy of directed connectivity in the brain by increasing the balance between senders and receivers of neural signals.