Abstract Fast radio bursts (FRBs) are bright, millisecond-duration radio transients originating from sources at extragalactic distances1, the origin of which is unknown. Some FRB sources emit repeat bursts, ruling out cataclysmic origins for those events2,3,4. Despite searches for periodicity in repeat burst arrival times on timescales from milliseconds to many days2,5,6,7, these bursts have hitherto been observed to appear sporadically and—although clustered8—without a regular pattern.