How tightly clustered are the CHIME-detected FRB repeats?
You'd be right to be a little suspicious if CHIME had just detected two events. Fortunately, that's not typically the detection criterion for a repeating FRB. In the case you're talking about, FRB 180814.J0422+73 (Amiri et al. 2019 for the CHIME/FRB Collaboration), six bursts were detected from one particular region, with only 18 total bursts detected in that pre-commissioning phase (so 13 sources total). That high a fraction of bursts coming from a very small part of the sky is enough to raise some eyebrows.
You're also right that CHIME's angular resolution is not enough to localize the bursts to within a galaxy-sized region at this distance ($\sim500$ Mpc), as CHIME folks will readily admit. To lend more credence to a repeating source, long-baseline interferometry is required, involving either follow-up observations or digging through archival datasets. The latter was the mode of choice for FRB 180814.J0422+73, as the group looked at old survey data from the Very Large Array (VLA) Sky Survey (VLASS) and the NRAO VLA Sky Survey
(NVSS). They found five sources in the region with fluxes close to what would be expected from this source. It's insufficient to say which one corresponds to the host galaxy, but it's likely that one of the five is responsible.
At the moment, the CHIME team is trying to improve its localization capabilities by adding &quot;outrigger&quot; telescopes in the United States and Canada, including one at the Green Bank Observatory. Ideally, this would reduce or eliminate the need for follow-up observations with other telescopes.