The origin of fast radio bursts (FRBs), millisecond-duration flashes of radio waves that are visible at distances of billions of light-years, remains an open astrophysical question. Here we report the detection of the multi-component FRB 20191221A with the Canadian Hydrogen Intensity Mapping Experiment Fast Radio Burst Project (CHIME/FRB), and the identification of a periodic separation of 216.8(1) ms between its components with a significance of 6.5 sigmas. The long (~ 3 s) duration and nine or more components forming the pulse profile make this source an outlier in the FRB population. We also report two additional FRBs, 20210206A and 20210213A, whose multi-component pulse profiles show some indication of periodic separations of 2.8(1) and 10.7(1) ms, respectively, suggesting the possible existence of a group of FRBs with complex and periodic pulse profiles. Such short periodicities provide strong evidence for a neutron-star origin of these events. Moreover, our detections favour emission arising from the neutron-star magnetosphere, as opposed to emission regions located further away from the star, as predicted by some models. Possible explanations for the observed periodicity include super-giant pulses from a neutron star that are possibly related to a magnetar outburst and interacting neutron stars in a binary system.
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