The purpose of this study is to investigate the effects of an oral psilocybin pulse regimen in cluster headache. Subjects will be randomized to receive oral placebo, low dose psilocybin, or high dose psilocybin in three experimental sessions, each separated by 5 days. Subjects will maintain a headache diary prior to, during, and after the pulse regimen in order to document headache frequency and intensity before, during, and after the pulse regimen. After at least 6 months from the last experimental session, subjects may be invited for a second round, in which they will be randomized to receive either low dose or high dose psilocybin. https://clinicaltrials.gov/ct2/show/NCT02981173