The nearest exoplanets to the Sun are our best possibilities for detailed characterization. We report the discovery of a compact multi-planet system of super-Earths orbiting the nearby red dwarf GJ 887, using radial velocity measurements. The planets have orbital periods of 9.3 and 21.8~days. Assuming an Earth-like albedo, the equilibrium temperature of the 21.8 day planet is approx 350 K; which is interior, but close to the inner edge, of the liquid-water habitable zone. We also detect a further unconfirmed signal with a period of 50 days which could correspond to a third super-Earth in a more temperate orbit. GJ 887 is an unusually magnetically quiet red dwarf with a photometric variability below 500 parts-per-million, making its planets amenable to phase-resolved photometric characterization.
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