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Fast radio bursts (FRBs) are extragalactic astrophysical transients 1 whose brightness requires emitters that are highly energetic yet compact enough to produce the short, millisecond-duration bursts. FRBs have thus far been detected at frequencies from 8 gigahertz (ref. 2 ) down to 300 megahertz (ref. 3 ), but lower-frequency emission has remained elusive. Some FRBs repeat 4-6 , and one of the most frequently detected, FRB 20180916B 7 , has a periodicity cycle of 16.35 days (ref. 8 ). Using simultaneous radio data spanning a wide range of wavelengths (a factor of more than 10), here we show that FRB 20180916B emits down to 120 megahertz, and that its activity window is frequency dependent (that is, chromatic). The window is both narrower and earlier at higher frequencies. Binary wind interaction models predict a wider window at higher frequencies, the opposite of our observations. Our full-cycle coverage shows that the 16.3-day periodicity is not aliased. We establish that low-frequency FRB emission can escape the local medium. For bursts of the same fluence, FRB 20180916B is more active below 200 megahertz than at 1.4 gigahertz. Combining our results with previous upper limits on the all-sky FRB rate at 150 megahertz, we find there are 3-450 FRBs in the sky per day above 50 Jy ms. Our chromatic results strongly disfavour scenarios in which absorption from strong stellar winds causes FRB periodicity. We demonstrate that some FRBs are found in 'clean' environments that do not absorb or scatter low-frequency radiation., (© 2021. The Author(s), under exclusive licence to Springer Nature Limited.)