I 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, ranging from 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. The method presented here compares observed stellar photometry with empirical stellar templates, incorporating prior knowledge about the structure of the Galaxy. The map can be queried or downloaded at http://argonaut.skymaps.info. I 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. The method presented here is not limited to the passbands of the Pan-STARRS 1 and 2MASS surveys, but may be extended to incorporate photometry from other optical and near-infrared surveys, such as WISE, Spitzer GLIMPSE, UKIDSS, SDSS, and in the future, LSST. The method can also be naturally extended to stellar kinematic data, such as that soon to be released by Gaia.