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 1.62 \pm 0.11 R _ { \oplus } super Earth on a 1.2 day period , a 1.269 ^ { +0.087 } _ { -0.089 } R _ { \oplus } super Earth on a 3.6 day period , and a 2.07 \pm 0.14 R _ { \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 .