The growth in efficiency of earth-abundant kesterite Cu2ZnSn(S,Se)4 (CZTSSe) solar cells has slowed, due in part to the intrinsic limitations imposed by the band tailing attributed primarily to I-II antisite exchange. In this study, density functional theory simulations show that when Ag is substituted for Cu to form kesterite Ag2ZnSnSe4 (AZTSe), the I-II isolated antisite formation energy becomes 3.7 times greater than in CZTSSe, resulting in at least an order of magnitude reduction in I-II antisite density. Experimental evidence of an optoelectronically improved material is also provided. Comparison of the low-temperature photoluminescence (PL) structure of Cu(In,Ga)Se2 (CIGSe), CZTSSe, and AZTSe shows that AZTSe has a shallow defect structure with emission significantly closer to the band edge than CZTSe. Existence of suppressed band tailing is found in the proximity of the room-temperature PL peak of AZTSe to its measured band gap. The results are consistent with AZTSe being a promising alternative to CZTSSe and CIGSe for thin film photovoltaics.