We calculate the shift current response, which has been identified as the dominant mechanism for the bulk photovoltaic effect, for the polar compounds LiAsS$_text{2}$, LiAsSe$_text{2}$, and NaAsSe$_text{2}$. We find that the magnitudes of the photovoltaic responses in the visible range for these compounds exceed the maximum response obtained for BiFeO$_text{3}$ by 10 - 20 times. We correlate the high shift current response with the existence of $p$ states at both the valence and conduction band edges, as well as the dispersion of these bands, while also showing that high polarization is not a requirement. With low experimental band gaps of less than 2 eV and high shift current response, these materials have potential for use as bulk photovoltaics.