We present a model of weak scale dark matter (DM) where the thermal DM density is set by the lepton asymmetry due to the presence of higher dimension lepton violating operators. In these models there is generically a separation between the annihilation cross section responsible for the relic abundance (through lepton violating operators) and the annihilation cross section that is relevant for the indirect detection of DM (through lepton preserving operators). This implies a perceived boost in the annihilation cross section in the Galaxy today relative to that derived for canonical thermal freeze-out, giving a natural explanation for the observed cosmic ray electron and positron excesses, without resorting to a Sommerfeld enhancement. These models motivate continued searches for DM with apparently nonthermal annihilation cross sections. The DM may also play a role in radiatively generating Majorana neutrino masses.