  The chalcogenide perovskite BaZrS$_3$ has attracted much attention as a
promising solar absorber for thin-film photovoltaics. Here, we use
first-principles calculations to evaluate its carrier transport and defect
properties. We find that BaZrS$_3$ has a phonon-limited electron mobility of 37
cm$^2$/Vs comparable to that in halide perovskites but lower hole mobility of
11 cm$^2$/Vs. The defect computations indicate that BaZrS$_3$ is intrinsically
n-type due to shallow sulfur vacancies, but that strong compensation by sulfur
vacancies will prevent attempts to make it p-type. We also establish that
BaZrS$_3$ is a defect-tolerant absorber with few low formation energy, deep
intrinsic defects. Among the deep defects, sulfur interstitials are the
strongest nonradiative recombination centers which in sulfur-rich conditions
would limit the carrier lifetime to 10 ns. Our work highlights the material's
intrinsic limitations in carrier mobility and suggests suppressing the
formation of sulfur interstitials to reach long carrier lifetime.
