Distributed Acoustic Sensing (DAS) leverages an ocean-bottom telecommunication fiber-optic cable into a densely-sampled massive array of strain sensors. We demonstrate DAS applications to Passive Acoustic Monitoring (PAM) through an experiment in Longyearbyen, Svalbard, Norway. We show that DAS can measure many types of signals generated by dynamics in the atmosphere, ocean, and solid earth. These include primary and secondary microseisms, Scholte waves, water-layer acoustic resonances, and seismic waves from earthquakes. In addition, we can trace the origin of primary microseisms back to distant storms a quarter of the way around the planet. We also find that the fjord acts as an amplifier for microseisms. Because DAS is capable of hydroacoustic monitoring with high spatial resolution over great distances, it can deliver great scientific value to ocean observation. We believe that DAS can and will become a valuable component of the Global Ocean Observing System.