  On 14 August 2019, the LIGO and Virgo Collaborations detected gravitational
waves from a black hole and a 2.6 solar mass compact object, possibly the first
neutron star -- black hole (NSBH) merger. In search of an optical counterpart,
the Dark Energy Survey (DES) obtained deep imaging of the entire 90 percent
confidence level localization area with Blanco/DECam 0, 1, 2, 3, 6, and 16
nights after the merger. Objects with varying brightness were detected by the
DES Pipeline and we systematically reduced the 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 full light curve simulations of supernovae and kilonovae as they
would appear in the DECam observations. Since the source class of the merger
was uncertain, we utilized an agnostic, three-component kilonova model based on
tidally-disrupted NS ejecta properties to quantify our detection efficiency of
a counterpart if the merger included a NS. 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 $2\sigma$ level.
Furthermore, we estimate that our background reduction methods are capable of
associating gravitational wave signals with a detected electromagnetic
counterpart at the $4\sigma$ level in $95\%$ of future follow-up observations.
