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 Space Telescope observations to measure some of the basic host galaxy properties. We compare and contrast the X-ray emission and host galaxy of GRB 100316D to a subsample of GRB-SNe. GRB 100316D is unlike the majority of GRB-SNe in its X-ray evolution, but resembles rather GRB 060218, and we find that these two events have remarkably similar high energy prompt emission properties. Comparison of the host galaxies of GRB-SNe demonstrates, however, that there is a great diversity in the environments in which GRB-SNe can be found. GRB 100316D is an important addition to the currently sparse sample of spectroscopically confirmed GRB-SNe, from which a better understanding of long GRB progenitors and the GRB-SN connection can be gleaned.