  The nature of fast radio bursts (FRBs) remains enigmatic. Highly energetic
radio pulses of millisecond duration, FRBs are observed with dispersion
measures consistent with an extragalactic source. A variety of models have been
proposed to explain their origin. One popular class of theorized FRB progenitor
is the coalescence of compact binaries composed of neutron stars and/or black
holes. Such coalescence events are strong gravitational-wave emitters. We
demonstrate that measurements made by the LIGO and Virgo gravitational-wave
observatories can be leveraged to severely constrain the validity of FRB binary
coalescence models. Existing measurements constrain the binary black hole rate
to approximately $5\%$ of the FRB rate, and results from Advanced LIGO's O1 and
O2 observing runs may place similarly strong constraints on the fraction of
FRBs due to binary neutron star and neutron star--black hole progenitors.
