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Advanced LIGO and Virgo have reported 90 confident gravitational-wave (GW) observations from compact-binary coalescences from their three observation runs. In addition, numerous subthreshold gravitational-wave candidates have been identified. Binary neutron star (BNS) mergers can produce gravitational waves and short-gamma ray bursts, as confirmed by GW170817/GRB 170817A. There may be electromagnetic counterparts recorded in archival observations associated with subthreshold gravitational-wave candidates. The CHIME/FRB Collaboration has reported the first large sample of fast radio bursts (FRBs), millisecond radio transients detected up to cosmological distances; a fraction of these may be associated with BNS mergers. This work searches for coincident gravitational waves and FRBs from BNS mergers using candidates from the fourth-Open Gravitational-wave Catalog (4-OGC) and the first CHIME/FRB catalog. We use a ranking statistic for GW/FRB association which combines the gravitational-wave detection statistic with the odds of temporal and spatial association. We analyze gravitational-wave candidates and non-repeating FRBs from 2019 April 1 to 2019 July 1, when both the Advanced LIGO/Virgo gravitational-wave detectors and the CHIME radio telescope were observing. The most significant coincident candidate has a false alarm rate of 0.29 per observation time, which is consistent with a null observation. The null results imply, at most, $\mathcal{O}(0.01)\%$ - $\mathcal{O}(1)\%$ of FRBs are produced from the BNS mergers.