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Instabilities, where initially small fluctuations seed the formation of large-scale structures, govern the dynamics in various fluid flows. The Rayleigh-Taylor instability (RTI) is an iconic example that leads to the development of mushroom-shaped incursions when immiscible fluids are accelerated into each other. RTI drives structure formation throughout science and engineering including table-top oil and water mixtures; supernova explosions; and inertial confinement fusion.  Despite its ubiquity, controlled laboratory RTI experiments are technically challenging. Here we report the experimental observation of RTI in an initially phase-separated binary superfluid consisting of a two-component Bose-Einstein condensate of $\Na23$ atoms. We induce the RTI at the interface between these components using a magnetic gradient force (i.e. the Stern-Gerlach effect) to press the components together and observe the growth of mushroom-like structures. The interface becomes stable when the components are pulled apart, and we spectroscopically measure the dispersion relation of the ``ripplon'' interface modes.