We know now from radial velocity surveys and transit space missions that planets only a few times more massive than our Earth are frequent around solar-type stars. Fundamental questions about their formation history, physical properties, internal structure, and atmosphere composition are, however, still to be solved. We present here the detection of a system of four low-mass planets around the bright (V=5.5) and close-by (6.5pc) star HD 219134. This is the first result of the Rocky Planet Search programme with HARPS-N on the Telescopio Nazionale Galileo in La Palma. The inner planet orbits the star in 3.0935+/-0.0003-days, on a quasi-circular orbit with a semi-major axis of 0.0382+/-0.0003AU. Spitzer observations allowed us to detect the transit of the planet in front of the star making HD 219134 b the nearest known transiting planet to date.