Kepler-20 is a solar-type star (V=12.5) hosting a compact system of five transiting planets, all packed within the orbital distance of Mercury in our own solar system. A transition from rocky to gaseous planets with a planetary transition radius of ~1.6R_{Earth} has recently been proposed by several articles in the literature. Kepler-20b (R_p~1.9R_{Earth}) has a size beyond this transition radius; however, previous mass measurements were not sufficiently precise to allow definite conclusions to be drawn regarding its composition. We present new mass measurements of three of the planets in the Kepler-20 system that are facilitated by 104 radial velocity measurements from the HARPS-N spectrograph and 30 archival Keck/HIRES observations, as well as an updated photometric analysis of the Kepler data and an asteroseismic analysis of the host star (M=0.948+/-0.051M{Sun} and R=0.964+/-0.018R{Sun}). Kepler-20b is a 1.868-0.034_^+0.066^R_{Earth} planet in a 3.7day period with a mass of 9.70-1.44_^+1.41^M_{Earth}, resulting in a mean density of 8.2-1.3_^+1.5^g/cm^3^, indicating a rocky composition with an iron-to-silicate ratio consistent with that of the Earth. This makes Kepler-20b the most massive planet with a rocky composition found to date. Furthermore, we report the discovery of an additional non-transiting planet with a minimum mass of 19.96_-3.61_^+3.08^M_{Earth}_ and an orbital period of ~34days in the gap between Kepler-20f (P~11days) and Kepler-20d (P~78days).