  We perform a search for stellar streams around the Milky Way using the first
three years of multi-band optical imaging data from the Dark Energy Survey
(DES). We use DES data covering $\sim 5000$ sq. deg. to a depth of $g > 23.5$
with a relative photometric calibration uncertainty of $< 1 \%$. This data set
yields unprecedented sensitivity to the stellar density field in the southern
celestial hemisphere, enabling the detection of faint stellar streams to a
heliocentric distance of $\sim 50$ kpc. We search for stellar streams using a
matched-filter in color-magnitude space derived from a synthetic isochrone of
an old, metal-poor stellar population. Our detection technique recovers four
previously known thin stellar streams: Phoenix, ATLAS, Tucana III, and a
possible extension of Molonglo. In addition, we report the discovery of eleven
new stellar streams. In general, the new streams detected by DES are fainter,
more distant, and lower surface brightness than streams detected by similar
techniques in previous photometric surveys. As a by-product of our stellar
stream search, we find evidence for extra-tidal stellar structure associated
with four globular clusters: NGC 288, NGC 1261, NGC 1851, and NGC 1904. The
ever-growing sample of stellar streams will provide insight into the formation
of the Galactic stellar halo, the Milky Way gravitational potential, as well as
the large- and small-scale distribution of dark matter around the Milky Way.
