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We demonstrate the blind interferometric detection and localization of two fast radio bursts (FRBs) with 2- and 25-arcsecond precision on the 400-m baseline between the Canadian Hydrogen Intensity Mapping Experiment (CHIME) and the CHIME Pathfinder. In the same spirit as very long baseline interferometry (VLBI), the telescopes were synchronized to separate clocks, and the channelized voltage (herein referred to as "baseband") data were saved to disk with correlation performed offline. The simultaneous wide field of view and high sensitivity required for blind FRB searches implies a high data rate -- 6.5 terabits per second (Tb/s) for CHIME and 0.8 Tb/s for the Pathfinder. Since such high data rates cannot be continuously saved, we buffer data from both telescopes locally in memory for $\approx 40$ s, and write to disk upon receipt of a low-latency trigger from the CHIME Fast Radio Burst Instrument (CHIME/FRB). The $\approx200$ deg$^2$ field of view of the two telescopes allows us to use in-field calibrators to synchronize the two telescopes without needing either separate calibrator observations or an atomic timing standard. In addition to our FRB observations, we analyze bright single pulses from the pulsars B0329+54 and B0355+54 to characterize systematic localization errors. Our results demonstrate the successful implementation of key software, triggering, and calibration challenges for CHIME/FRB Outriggers: cylindrical VLBI outrigger telescopes which, along with the CHIME telescope, will localize thousands of single FRB events to 50 milliarcsecond precision.