GW190814 was a compact object binary coalescence detected in gravitational waves by Advanced LIGO and Advanced Virgo that garnered exceptional community interest due to its excellent localization and the uncertain nature of the binarys lighter-mass component (either the heaviest known neutron star, or the lightest known black hole). Despite extensive follow up observations, no electromagnetic counterpart has been identified. Here we present new radio observations of 75 galaxies within the localization volume at $Delta tapprox 35-266$ days post-merger. Our observations cover $sim32$% of the total stellar luminosity in the final localization volume and extend to later timescales than previously-reported searches, allowing us to place the deepest constraints to date on the existence of a radio afterglow from a highly off-axis relativistic jet launched during the merger (assuming that the merger occurred within the observed area). For a viewing angle of $sim46^{circ}$ (the best-fit binary inclination derived from the gravitational wave signal) and assumed electron and magnetic field energy fractions of $epsilon_e=0.1$ and $epsilon_B=0.01$, we can rule out a typical short gamma-ray burst-like Gaussian jet with isotropic-equivalent kinetic energy $2times10^{51}$ erg propagating into a constant density medium $ngtrsim0.01$ cm$^{-3}$. These are the first limits resulting from a galaxy-targeted search for a radio counterpart to a gravitational wave event, and we discuss the challenges, and possible advantages, of applying similar search strategies to future events using current and upcoming radio facilities.
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