High resolution transit spectroscopy has proven to be a reliable technique for the characterization of the chemical composition of exoplanet atmospheres . Taking advantage of the broad spectral coverage of the CARMENES spectrograph , we initiated a survey aimed at characterizing a broad range of planetary systems . Here , we report our observations of three transits of GJ 3470 b \xspace with CARMENES in search of He ( 2 ^ { 3 } S ) absorption . On one of the nights , the He i region was heavily contaminated by OH ^ { - } telluric emission and , thus , it was not useful for our purposes . The remaining two nights had a very different signal-to-noise ratio ( S/N ) due to weather . They both indicate the presence of He ( 2 ^ { 3 } S ) absorption in the transmission spectrum of GJ 3470 b \xspace , although a statistically valid detection can only be claimed for the night with higher S/N . For that night , we retrieved a 1.5 \pm 0.3 % absorption depth , translating into a R _ { p } ( \lambda ) / R _ { p } = 1.15 \pm 0.14 at this wavelength . Spectro-photometric light curves for this same night also indicate the presence of extra absorption during the planetary transit with a consistent absorption depth . The He ( 2 ^ { 3 } S ) absorption is modeled in detail using a radiative transfer code , and the results of our modeling efforts are compared to the observations . We find that the mass-loss rate , \dot { M } , is confined to a range of 3 \times 10 ^ { 10 } g s ^ { -1 } for T = 6000 K to 10 \times 10 ^ { 10 } g s ^ { -1 } for T = 9000 K. We discuss the physical mechanisms and implications of the He i detection in GJ 3470 b \xspace and put it in context as compared to similar detections and non-detections in other Neptune-size planets . We also present improved stellar and planetary parameter determinations based on our visible and near-infrared observations .