We report on the discovery of three transiting planets around GJ 9827. The planets have radii of 1.75 ± 0.18, 1.36 ± 0.14, and {2.11}-0.21+0.22 R ⊕, and periods of 1.20896, 3.6480, and 6.2014 days, respectively. The detection was made in Campaign 12 observations as part of our K2 survey of nearby stars. GJ 9827 is a V = 10.39 mag K6V star at a distance of 30.3 ± 1.6 parsecs and the nearest star to be found hosting planets by Kepler and K2. The radial velocity follow-up, high-resolution imaging, and detection of multiple transiting objects near commensurability drastically reduce the false positive probability. The orbital periods of GJ 9827 b, c, and d planets are very close to the 1:3:5 mean motion resonance. Our preliminary analysis shows that GJ 9827 planets are excellent candidates for atmospheric observations. Besides, the planetary radii span both sides of the rocky and gaseous divide, hence the system will be an asset in expanding our understanding of the threshold.