  The coalescence of a binary neutron star (BNS) pair is expected to produce
gravitational waves (GW) and electromagnetic (EM) radiation, both of which may
be detectable with currently available instruments. We describe a search for a
theoretically predicted r-process optical transient from these mergers, dubbed
the kilonova (KN), using griz broadband data from the Dark Energy Survey
Supernova Program (DES-SN). Some models predict KNe to be redder,
shorter-lived, and dimmer than supernovae (SNe), but at present the event rate
of KNe is poorly constrained. We simulate observations of KN and SN light
curves with the Monte-Carlo simulation code SNANA to optimize selection
requirements, determine search efficiency, and predict SN backgrounds. We also
perform an analysis using fake point sources on images to account for anomalous
efficiency losses from difference-imaging on bright low-redshift galaxies. Our
analysis of the first two seasons of DES-SN data results in 0 events, and is
consistent with our prediction of 1.1 background events based on simulations of
SN. Given our simulation prediction, there is a 33 percent chance of finding 0
events in the data. Assuming no underlying galaxy flux, our search sets 90
percent upper limits on the KN volumetric rate of $1.0\times10^7$ Gpc$^{-3}$
yr$^{-1}$ for the dimmest KN model we consider (peak i-band absolute magnitude
$M_i=-11.4$ mag) and $2.4\times10^4$ Gpc$^{-3}$ yr$^{-1}$ for the brightest
($M_i=-16.2$ mag). Accounting for efficiency loss from host galaxy Poisson
noise, these limits are 1.1 times higher; accounting for anomalous subtraction
artifacts on bright galaxies, these limits are ~3 times higher. While previous
KN searches were based on triggered follow-up, this analysis is the first
untriggered optical KN search and informs selection requirements and strategies
for future KN searches and GW follow-up observations.
