We report the discovery of three small transiting planets orbiting GJ 9827, a bright (K = 7.2) nearby late K-type dwarf star. GJ 9827 hosts a super Earth on a 1.2 day period, a super Earth on a 3.6 day period, and a $R_{\rm \oplus}$ super Earth on a 6.2 day period. The radii of the planets transiting GJ 9827 span the transition between predominantly rocky and gaseous planets, and GJ 9827 b and c fall in or close to the known gap in the radius distribution of small planets between these populations. At a distance of 30 parsecs, GJ 9827 is the closest exoplanet host discovered by K2 to date, making these planets well-suited for atmospheric studies with the upcoming James Webb Space Telescope. The GJ 9827 system provides a valuable opportunity to characterize interior structure and atmospheric properties of coeval planets spanning the rocky to gaseous transition.

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