We present submillimeter observations of the z= 3.653 quasar SDSS 160705+533558 together with data in the optical and infrared. The object is unusually bright in the far-IR and submillimeter with an IR luminosity of ~1014 L sun. We ascribe this luminosity to a combination of active galactic nucleus (AGN) and starburst emission, with the starburst forming stars at a rate of a few thousand solar masses per year. Submillimeter Array imaging observations with a resolution ~1'' show that the submillimeter (850 μm) emission is extended on scales of 10- 35 kpc and is offset from the optical position by ~10 kpc. This morphology is dissimilar to that found in submillimeter galaxies, which are generally unresolved or marginally resolved on arcsecond scales, or submillimeter-luminous AGNs where the AGN lies at the peak of the submillimeter or molecular emission. The simplest explanation is that the object is in the early stages of a merger between a gas-rich galaxy, which hosts the starburst, and a gas-poor AGN-host galaxy, which is responsible for the quasar emission. It is also possible that jet-induced star formation might contribute to the unusual morphology.