We present a method to infer reddenings and distances to stars based only on their broad-band photometry, and show how this method can be used to produce a three-dimensional (3D) dust map of the Galaxy. Our method samples from the full probability density function of distance, reddening, and stellar type for individual stars, as well as the full uncertainty in reddening as a function of distance in the 3D dust map. We incorporate prior knowledge of the distribution of stars in the Galaxy and the detection limits of the survey. For stars in the Pan-STARRS 1 (PS1) 3π survey, we demonstrate that our reddening estimates are unbiased and accurate to ~0.13 mag in E(B – V) for the typical star. Based on comparisons with mock catalogs, we expect distances for main-sequence stars to be constrained to within ~20%-60%, although this range can vary, depending on the reddening of the star, the precise stellar type, and its position on the sky. A later paper will present a 3D map of dust over the three quarters of the sky surveyed by PS1. Both the individual stellar inferences and the 3D dust map will enable a wealth of Galactic science in the plane. The method we present is not limited to the passbands of the PS1 survey but may be extended to incorporate photometry from other surveys, such as the Two Micron All Sky Survey, the Sloan Digital Sky Survey (where available), and in the future, LSST and Gaia. ; Astronomy