  We report the discovery of Antlia B, a faint dwarf galaxy at a projected
distance of $\sim$72 kpc from NGC 3109 ($M_{V}$$\sim$$-$15 mag), the primary
galaxy of the NGC 3109 dwarf association at the edge of the Local Group. The
tip of the red giant branch distance to Antlia B is $D$=1.29$\pm$0.10 Mpc,
which is consistent with the distance to NGC 3109. A qualitative analysis
indicates the new dwarf's stellar population has both an old, metal poor red
giant branch ($\gtrsim$10 Gyr, [Fe/H]$\sim$$-$2), and a younger blue population
with an age of $\sim$200-400 Myr, analogous to the original Antlia dwarf,
another likely satellite of NGC 3109. Antlia B has \ion{H}{1} gas at a velocity
of $v_{helio,HI}$=376 km s$^{-1}$, confirming the association with NGC 3109
($v_{helio}$=403 km s$^{-1}$). The HI gas mass
(M$_{HI}$=2.8$\pm$0.2$\times$10$^{5}$ M$_{\odot}$), stellar luminosity
($M_{V}$=$-$9.7$\pm$0.6 mag) and half light radius ($r_{h}$=273$\pm$29 pc) are
all consistent with the properties of dwarf irregular and dwarf spheroidal
galaxies in the Local Volume, and is most similar to the Leo P dwarf galaxy.
The discovery of Antlia B is the initial result from a Dark Energy Camera
survey for halo substructure and faint dwarf companions to NGC 3109 with the
goal of comparing observed substructure with expectations from the
$\Lambda$+Cold Dark Matter model in the sub-Milky Way regime.
