On 14 August 2019, the LIGO and Virgo Collaborations alerted the astronomical community of a high significance detection of gravitational waves and classified the source as a neutron star - black hole (NSBH) merger, the first event of its kind. In search of an optical counterpart, the Dark Energy Survey (DES) Gravitational Wave Search and Discovery Team performed the most thorough and accurate analysis to date, targeting the entire 90 percent confidence level localization area with Blanco/DECam 0, 1, 2, 3, 6, and 16 nights after the merger was detected. Objects with varying brightness were detected by the DES Search and Discovery Pipeline and we systematically reduced the list of candidate counterparts through catalog matching, light curve properties, host-galaxy photometric redshifts, SOAR spectroscopic follow-up observations, and machine-learning-based photometric classification. All candidates were rejected as counterparts to the merger. To quantify the sensitivity of our search, we applied our selection criteria to simulations of supernovae and kilonovae as they would appear in the DECam observations. Since there are no explicit light curve models for NSBH mergers, we characterize our sensitivity with binary NS models that are expected to have similar optical signatures as NSBH mergers. We find that if a kilonova occurred during this merger, configurations where the ejected matter is greater than 0.07 solar masses, has lanthanide abundance less than $10^{-8.56}$, and has a velocity between $0.18c$ and $0.21c$ are disfavored at the $2sigma$ level. Furthermore, we estimate that our background reduction methods are capable of associating gravitational wave signals with a detected electromagnetic counterpart at the $4sigma$ level in $95%$ of future follow-up observations.
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