  We search for gravitational-wave transients associated with fast radio bursts
(FRBs) detected by the Canadian Hydrogen Intensity Mapping Experiment Fast
Radio Burst Project (CHIME/FRB), during the first part of the third observing
run of Advanced LIGO and Advanced Virgo (1 April 2019 15:00 UTC-1 Oct 2019
15:00 UTC). Triggers from 22 FRBs were analyzed with a search that targets
compact binary coalescences with at least one neutron star component. A
targeted search for generic gravitational-wave transients was conducted on 40
FRBs. We find no significant evidence for a gravitational-wave association in
either search. Given the large uncertainties in the distances of the FRBs
inferred from the dispersion measures in our sample, however, this does not
conclusively exclude any progenitor models that include emission of a
gravitational wave of the types searched for from any of these FRB events. We
report $90\%$ confidence lower bounds on the distance to each FRB for a range
of gravitational-wave progenitor models. By combining the inferred maximum
distance information for each FRB with the sensitivity of the
gravitational-wave searches, we set upper limits on the energy emitted through
gravitational waves for a range of emission scenarios. We find values of order
$10^{51}$-$10^{57}$ erg for a range of different emission models with central
gravitational wave frequencies in the range 70-3560 Hz. Finally, we also found
no significant coincident detection of gravitational waves with the repeater,
FRB 20200120E, which is the closest known extragalactic FRB.
