  We report on the first star discovered to host a planet detected by radial
velocity (RV) observations obtained within the CARMENES survey for exoplanets
around M dwarfs. HD 147379 ($V = 8.9$ mag, $M = 0.58 \pm 0.08$ M$_{\odot}$), a
bright M0.0V star at a distance of 10.7 pc, is found to undergo periodic RV
variations with a semi-amplitude of $K = 5.1\pm0.4$ m s$^{-1}$ and a period of
$P = 86.54\pm0.06$ d. The RV signal is found in our CARMENES data, which were
taken between 2016 and 2017, and is supported by HIRES/Keck observations that
were obtained since 2000. The RV variations are interpreted as resulting from a
planet of minimum mass $m_{\rm p}\sin{i} = 25 \pm 2$ M$_{\oplus}$, 1.5 times
the mass of Neptune, with an orbital semi-major axis $a = 0.32$ au and low
eccentricity ($e < 0.13$). HD 147379b is orbiting inside the temperate zone
around the star, where water could exist in liquid form. The RV time-series and
various spectroscopic indicators show additional hints of variations at an
approximate period of 21.1d (and its first harmonic), which we attribute to the
rotation period of the star.
