On 2019 August 14 the Laser Interferometer Gravitational Wave Observatory (LIGO) and the Virgo gravitational wave interferometer announced the detection of a binary merger, S190814bv, with a low false alarm rate of about 1 in 1.6x10^25^yr, a distance of 267+/-52Mpc, a 90% (50%) localization region of about 23 (5) deg^2^, and a probability of being a neutron star-black hole (NS-BH) merger of >99%. The LIGO/Virgo Collaboration (LVC) defines NS-BH such that the lighter binary member has a mass of <3M_{sun}_ and the more massive one has >5M_{sun}_, and this classification is in principle consistent with a BH-BH merger depending on the actual upper mass cutoff for neutron stars. Additionally, the LVC designated a probability that the merger led to matter outside the final BH remnant of <1%, suggesting that an electromagnetic (EM) counterpart is unlikely. Here we report our optical follow-up observations of S190814bv using the Magellan Baade 6.5m telescope to target all 96 galaxies in the Galaxy List for the Advanced Detector Era catalog within the 50% localization volume (representing about 70% of the integrated luminosity within this region). No counterpart was identified to a median 3{sigma} limiting magnitude of i=22.2 (M_i_~-14.9mag), comparable to the brightness of the optical counterpart of the binary neutron star merger GW170817 at the distance of S190814bv; similarly, we can rule out an on-axis jet typical of short GRBs. However, we cannot rule out other realistic models, such as a kilonova with only ~0.01M_{sun}_ of lanthanide-rich material, or an off-axis jet with a viewing angle of {theta}_obs_>~15{deg}.