Background Oxygen inhalation aborts cluster headache attacks, and case reports show the effect of continuous positive airway pressure. The aim of this study was to investigate the prophylactic effect of continuous positive airway pressure in chronic cluster headache. Methods This was a randomized placebo-controlled triple-blind crossover study using active and sham continuous positive airway pressure treatment for chronic cluster headache. Patients entered a one month’s baseline period before randomly being assigned to two months’ active continuous positive airway pressure treatment followed by a four weeks’ washout period and two months’ sham continuous positive airway pressure or vice versa. Primary outcome measure was number of cluster headache attacks/week. Results Of the 30 included participants (12 males, median age 49.5 years, min-max 20–66 years), 25 completed both treatment/sham cycles (two discontinued, three lost to follow-up). The median number of cluster headache attacks per week was reduced from 8.25 (0.75–89.75) attacks to 6.25 (0–56.00) attacks for active continuous positive airway pressure and to 7.50 (0.50–43.75) attacks for sham continuous positive airway pressure, but there was no difference in active versus sham (p = 0.904). One patient had a serious adverse event during active treatment, none occurred during sham treatment. Conclusions Continuous positive airway pressure treatment did not reduce the number of cluster headache attacks compared to sham treatment in chronic cluster headache patients. Trial registration Clinicaltrials.gov NCT03397563