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We report the discovery of Antlia B, a faint dwarf galaxy at a projecteddistance of $\sim$72 kpc from NGC 3109 ($M_{V}$$\sim$$-$15 mag), the primarygalaxy of the NGC 3109 dwarf association at the edge of the Local Group. Thetip of the red giant branch distance to Antlia B is $D$=1.29$\pm$0.10 Mpc,which is consistent with the distance to NGC 3109. A qualitative analysisindicates the new dwarf's stellar population has both an old, metal poor redgiant branch ($\gtrsim$10 Gyr, [Fe/H]$\sim$$-$2), and a younger blue populationwith 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 velocityof $v_{helio,HI}$=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$29 pc) areall consistent with the properties of dwarf irregular and dwarf spheroidalgalaxies in the Local Volume, and is most similar to the Leo P dwarf galaxy.The discovery of Antlia B is the initial result from a Dark Energy Camerasurvey for halo substructure and faint dwarf companions to NGC 3109 with thegoal of comparing observed substructure with expectations from the$\Lambda$+Cold Dark Matter model in the sub-Milky Way regime.

Antlia B: A faint dwarf galaxy member of the NGC 3109 association