The meter-per-second precision achieved by today’s velocimeters enables us to search for 1−10 M⊕ planets in the habitable zone of cool stars. This paper reports on the detection of three planets orbiting GJ 163 (HIP 19394), a M3 dwarf monitored by our ESO/HARPS search for planets. We made use of the HARPS spectrograph to collect 150 radial velocities of GJ 163 over a period of eight years. We searched the radial-velocity time series for coherent signals and found five distinct periodic variabilities. We investigated the stellar activity and called into question the planetary interpretation for two signals. Before more data can be acquired we concluded that at least three planets are orbiting GJ 163. They have orbital periods of Pb = 8.632 ...