We report the Swift discovery of the nearby long, soft gamma-ray burst GRB 100316D, and the subsequent unveiling of its low-redshift host galaxy and associated supernova. We derive the redshift of the event to be z= 0.0591 ± 0.0001 and provide accurate astrometry for the gamma-ray burst (GRB) supernova (SN). We study the extremely unusual prompt emission with time-resolved γ-ray to X-ray spectroscopy and find that the spectrum is best modelled with a thermal component in addition to a synchrotron emission component with a low peak energy. The X-ray light curve has a remarkably shallow decay out to at least 800 s. The host is a bright, blue galaxy with a highly disturbed morphology and we use Gemini-South, Very Large Telescope and Hubble Spa...