Fast radio bursts (FRBs) are millisecond-duration flashes of radio waves that are visible at distances of billions of light-years. The nature of their progenitors and their emission mechanism remain open astrophysical questions. Here we report the detection of the multi-component FRB 20191221A 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. Such short periodicity provides strong evidence for a neutron-star origin of the event. Moreover, our detection favours emission arising from the neutron-star magnetosphere, as opposed to emission regions...