The discovery of a repeating fast radio burst (FRB) source1,2, FRB 121102, eliminated models involving cataclysmic events for this source. No other repeating FRB has hitherto been detected despite many recent discoveries and follow-ups3-5, suggesting that repeaters may be rare in the FRB population. Here we report the detection of six repeat bursts from FRB 180814.J0422+73, one of the 13 FRBs detected6 by the Canadian Hydrogen Intensity Mapping Experiment (CHIME) FRB project7 during its pre-commissioning phase in July and August 2018. These repeat bursts are consistent with its origin from a single position on the sky, with the same dispersion measure, about 189 parsecs per cubic centimetre. This line of sight traces approximately twice the expected Milky Way column density of free electrons, which implies an upper limit on the source redshift of 0.1, showing it to be closer to Earth by a factor of at least 2 than FRB 1211028. In some of the repeat bursts, we observe subpulse frequency structure, drifting and spectral variation reminiscent of that seen in FRB 1211029,10, suggesting similar emission mechanisms or propagation effects. This second repeater, found among the first few CHIME/FRB discoveries, suggests that there exists—and that CHIME/FRB and other wide-field, sensitive radio telescopes will find—a substantial population of repeating FRBs.