We report the results of our observing campaign on GRB140903A, a nearby (z=0.351) short duration (T90~0.3 s) gamma-ray burst discovered by Swift. We monitored the X-ray afterglow with Chandra up to 21 days after the burst, and detected a steeper decay of the X-ray flux after approximately 1 day. Continued monitoring at optical and radio wavelengths showed a similar decay in flux at nearly the same time, and we interpret it as evidence of a narrowly collimated jet. By using the standard fireball model to describe the afterglow evolution, we derive a jet opening angle of 5 deg and a collimation-corrected total energy release of 2E50 erg. We further discuss the nature of the GRB progenitor system. Three main lines disfavor a massive star progenitor: the properties of the prompt gamma-ray emission, the age and low star-formation rate of the host galaxy, and the lack of a bright supernova. We conclude that this event was likely originated by a compact binary merger.