Fast radio bursts (FRBs) are bright, millisecond-duration radio transients originating from extragalactic distances 1 . Their origin is unknown. Some FRB sources emit repeat bursts, ruling out cataclysmic origins for those events [2][3][4] . Despite searches for periodicity in repeat burst arrival times on time scales from milliseconds to many days 2, 5-7 , these bursts have hitherto been observed to appear sporadically, and though clustered 8 , without a regular pattern. Here we report the detection of a 16.35 ± 0.18 day periodicity from a repeating FRB 180916.J0158+65 detected by the Canadian Hydrogen Intensity Mapping Experiment Fast Radio Burst Project (CHIME/FRB) 4, 9 . In 28 bursts recorded from 16th September 2018 through 30th October 2019, we find that bursts arrive in a 4.0-day phase window, with some cycles showing no bursts, and some showing multiple bursts, within CHIME's limited daily exposure. Our results suggest a mechanism for periodic modulation either of the burst emission itself, or through external amplification or absorption, and disfavour models invoking purely sporadic processes.Last year the CHIME/FRB collaboration reported the discovery of eight new repeating FRB sources 4 , including FRB 180916.J0158+65, which was recently localized to a star-forming region in a nearby massive spiral galaxy at redshift 0.0337±0.0002 10 . From September 2018 to November 2019, CHIME/FRB has detected a total of 28 bursts from FRB 180916.J0158+65, which remains the most active source from this recent CHIME/FRB repeater sample. The barycentric arrival times for the 28 bursts (including those has been published before) from FRB 180916.J0158+65, corrected for delays from pulse dispersion, are listed in Extended Data Table 1.To search for periodicity, the burst arrival times (spanning a 400-day time range) were folded with different periods from 1.57 to 62.8 days (see Methods), with a Pearson's χ 2 test applied to each resulting profile with 8 phase bins 11 . A reduced χ 2 1 with respect to a uniform distribution indicates a periodicity unlikely to arise by chance. Furthermore, to account for the possible non-Poissonian statistics of the bursts 12 , we have applied the search with different weighting schemes that consider clustered bursts of different time range to be correlated events (see Methods).Searches with different weightings return periodograms of similar shape and have the same primary peak with significance varying between 3.5 − 8σ. As an example, the reduced χ 2 versus period using a weighting that counts only active days instead of individual events is shown in Figure 1a. A distinct peak is detected at 16.35 ± 0.18 days, with
