Abstract We report on the discovery of FRB 20200120E, a repeating fast radio burst (FRB) with a low dispersion measure (DM) detected by the Canadian Hydrogen Intensity Mapping Experiment FRB project. The source DM of 87.82 pc cm⁻³ is the lowest recorded from an FRB to date, yet it is significantly higher than the maximum expected from the Milky Way interstellar medium in this direction (∼50 pc cm⁻³). We have detected three bursts and one candidate burst from the source over the period 2020 January–November. The baseband voltage data for the event on 2020 January 20 enabled a sky localization of the source to within ≃14 arcmin² (90% confidence). The FRB localization is close to M81, a spiral galaxy at a distance of 3.6 Mpc. The FRB appears on the outskirts of M81 (projected offset ∼20 kpc) but well inside its extended H i and thick disks. We empirically estimate the probability of a chance coincidence with M81 to be <10⁻². However, we cannot reject a Milky Way halo origin for the FRB. Within the FRB localization region, we find several interesting cataloged M81 sources and a radio point source detected in the Very Large Array Sky Survey. We search for prompt X-ray counterparts in Swift Burst Alert Telescope and Fermi/GBM data, and, for two of the FRB 20200120E bursts, we rule out coincident SGR 1806−20-like X-ray bursts. Due to the proximity of FRB 20200120E, future follow-up for prompt multiwavelength counterparts and subarcsecond localization could be constraining of proposed FRB models.