We present a map of the dust reddening to 4.5 kpc derived from Pan-STARRS1 stellar photometry. The map covers almost the entire sky north of declination -30° at a resolution of 7'-14', and is based on the estimated distances and reddenings to more than 500 million stars. The technique is designed to map dust in the Galactic plane, where many other techniques are stymied by the presence of multiple dust clouds at different distances along each line of sight. This reddening-based dust map agrees closely with the Schlegel et al. (SFD) far-infrared emission-based dust map away from the Galactic plane, and the most prominent differences between the two maps stem from known limitations of SFD in the plane. We also compare the map with Planck, finding likewise good agreement in general at high latitudes. The use of optical data from Pan-STARRS1 yields reddening uncertainty as low as 25 mmag E(B - V).