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Small low-mass stars are favourable targets for the detection of rockyhabitable planets. In particular, planetary systems in the solar neighbourhoodare interesting and suitable for precise characterisation. The Red Dotscampaigns seek to discover rocky planets orbiting nearby low-mass stars. The2018 campaign targeted GJ 1061, which is the 20$^{\rm th}$ nearest star to theSun. For three consecutive months we obtained nightly, high-precision radialvelocity measurements with the HARPS spectrograph. We analysed these datatogether with archival HARPS data. We report the detection of three planetcandidates with periods of $3.204\pm 0.001$, $6.689\pm 0.005$ and $13.03\pm0.03$ days, which is close to 1:2:4 period commensurability. After severalconsiderations related to the properties of the noise and sampling, we concludethat a 4$^{\rm th}$ signal is most likely explained by stellar rotation,although it may be due to a planet. The proposed three-planet system (and thepotential four-planet solution) is long-term dynamically stable. Planet-planetgravitational interactions are below our current detection threshold. Theminimum masses of the three planets range from $1.4\pm 0.2$ to $1.8\pm 0.3$M$_\oplus$. Planet d, with $m \sin i = 1.68\pm0.25$ M$_\oplus$, receives asimilar amount of energy as Earth receives from the Sun. Consequently it lieswithin the liquid-water habitable zone of the star and has a similarequilibrium temperature to Earth. GJ 1061 has very similar properties toProxima Centauri but activity indices point to lower levels of stellaractivity.

Red Dots: A temperate 1.5 Earth-mass planet in a compact multi-terrestrial planet system around GJ1061