BaZrS3, a prototypical chalcogenide perovskite, has been shown to possess a direct band gap, an exceptionally strong near band edge light absorption, and good carrier transport. Coupled with its great stability, non-toxicity with earth abundant elements, it is thus a promising candidate for thin film solar cells. However, its reported band gap in the range of 1.7-1.8 eV is larger than the optimal value required to reach the Shockley-Queisser limit of a single junction solar cell. Here we report the synthesis of Ba(Zr1-xTix)S3 perovskite compounds with a reduced band gap. It is found that Ti alloying is extremely effective in band gap reduction of BaZrS3: a mere 4 at% alloying decreases the band gap from 1.78 to 1.51 eV, resulting in a theoretical maximum power conversion efficiency of 32%. Higher Ti-alloying concentration is found to destabilize the distorted chalcogenide perovskite phase.