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We present here the detection of a system of four low-mass planets around the bright (V=5.5) and close-by (6.5 pc) star HD219134. This is the first result of the Rocky Planet Search program with HARPS-N on the TNG in La Palma. The inner planet orbits the star in 3.0937 +/-0.0004 days, on a quasi-circular orbit with a semi-major axis of 0.0382 +/- 0.0003 AU. Spitzer observations allowed us to detect the transit of the planet in front of the star making HD219134b the nearest known transiting planet to date. From the amplitude of the radial-velocity variation (2.33 +/- 0.24 m/s) and observed depth of the transit (359 +/- 38 ppm), the planet mass and radius are estimated to be 4.46 +/- 0.47 M_{\oplus} and 1.606 +/- 0.086 R_{\oplus} leading to a mean density of 5.89 +/- 1.17 g/cc, suggesting a rocky composition. One additional planet with minimum mass of 2.67 +/- 0.59 M_{\oplus} moves on a close-in, quasi-circular orbit with a period of 6.765 +/- 0.005 days. The third planet in the system has a period of 46.78 +/- 0.16 days and a minimum mass of 8.7 +/- 1.1 M{\oplus}, at 0.234 +/- 0.002 AU from the star. Its eccentricity is 0.32 +/- 0.14. The period of this planet is close to the rotational period of the star estimated from variations of activity indicators (42.3 +/- 0.1 days). The planetary origin of the signal is, however, the preferred solution as no indication of variation at the corresponding frequency is observed for activity-sensitive parameters. Finally, a fourth additional longer-period planet of mass of 62 +/- 6 M_{\oplus} orbits the star in 1190 days, on an eccentric orbit (e=0.27 +/- 0.11) at a distance of 2.14 +/- 0.27 AU.