The meter-per-second precision achieved by today velocimeters enables the search for 1-10 M_Earth planets in the habitable zone of cool stars. This paper reports on the detection of 3 planets orbiting GJ163 (HIP19394), a M3 dwarf monitored by our ESO/HARPS search for planets. We made use of the HARPS spectrograph to collect 150 radial velocities of GJ163 over a period of 8 years. We searched the RV time series for coherent signals and found 5 distinct periodic variabilities. We investigated the stellar activity and casted doubts on the planetary interpretation for 2 signals. Before more data can be acquired we concluded that at least 3 planets are orbiting GJ163. They have orbital periods of P_b=8.632+-0.002, P_c=25.63+-0.03 and P_d=604+-8 days and minimum masses msini = 10.6+-0.6, 6.8+-0.9, and 29+-3 M_Earth, respectively. We hold our interpretations for the 2 additional signals with periods P_(e)=19.4 and P_(f)=108 days. The inner pair presents an orbital period ratio of 2.97, but a dynamical analysis of the system shows that it lays outside the 3:1 mean motion resonance. GJ163c, in particular, is a super-Earth with an equilibrium temperature of T_eq = (302+-10) (1-A)^(1/4) K and may lie in the so called habitable zone for albedo values (A=0.34-0.89) moderately higher than that of Earth (A_Earth=0.2-0.3).
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