  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
binary's 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 $\Delta t\approx
35-266$ 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 $2\times10^{51}$ erg propagating into a
constant density medium $n\gtrsim0.01$ 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.
