We present a three-dimensional map of interstellar dust reddening, covering three-quarters of the sky out to a distance of several kiloparsecs, based on Pan-STARRS 1 and 2MASS photometry. The map reveals a wealth of detailed structure, from filaments to large cloud complexes. The map has a hybrid angular resolution, with most of the map at an angular resolution of 3.4 to 13.7, and a maximum distance resolution of ~25%. The three-dimensional distribution of dust is determined in a fully probabilistic framework, yielding the uncertainty in the reddening distribution along each line of sight, as well as stellar distances, reddenings and classifications for 800 million stars detected by Pan-STARRS 1. We demonstrate the consistency of our reddening estimates with those of two-dimensional emission-based maps of dust reddening. In particular, we find agreement with the Planck 353 GHz optical depth-based reddening map to within 0.05 mag in E(B-V) to a depth of 0.5 mag, and explore systematics at reddenings less than E(B-V) ~ 0.08 mag. We validate our per-star reddening estimates by comparison with reddening estimates for stars with both SDSS photometry and SEGUE spectral classifications, finding per-star agreement to within 0.1 mag out to a stellar E(B-V) of 1 mag. We compare our map to two existing three-dimensional dust maps, by Marshall et al. (2006) and Lallement et al. (2013), demonstrating our finer angular resolution, and better distance resolution compared to the former within ~3 kpc. The map can be queried or downloaded at http://argonaut.skymaps.info. We expect the three-dimensional reddening map presented here to find a wide range of uses, among them correcting for reddening and extinction for objects embedded in the plane of the Galaxy, studies of Galactic structure, calibration of future emission-based dust maps and determining distances to objects of known reddening.