NASAs Kepler Mission uses transit photometry to determine the frequency of earth-size planets in or near the habitable zone of Sun-like stars. The mission reached a milestone toward meeting that goal: the discovery of its first rocky planet, Kepler-10b. Two distinct sets of transit events were detected: 1) a 152 +/- 4 ppm dimming lasting 1.811 +/- 0.024 hours with ephemeris T[BJD]=2454964.57375+N*0.837495 days and 2) a 376 +/- 9 ppm dimming lasting 6.86 +/- 0.07 hours with ephemeris T[BJD]=2454971.6761+N*45.29485 days. Statistical tests on the photometric and pixel flux time series established the viability of the planet candidates triggering ground-based follow-up observations. Forty precision Doppler measurements were used to confirm that the short-period transit event is due to a planetary companion. The parent star is bright enough for asteroseismic analysis. Photometry was collected at 1-minute cadence for >4 months from which we detected 19 distinct pulsation frequencies. Modeling the frequencies resulted in precise knowledge of the fundamental stellar properties. Kepler-10 is a relatively old (11.9 +/- 4.5 Gyr) but otherwise Sun-like Main Sequence star with Teff=5627 +/- 44 K, Mstar=0.895 +/- 0.060 Msun, and Rstar=1.056 +/- 0.021 Rsun. Physical models simultaneously fit to the transit light curves and the precision Doppler measurements yielded tight constraints on the properties of Kepler-10b that speak to its rocky composition: Mpl=4.56 +/- 1.29 Mearth, Rpl=1.416 +/- 0.036 Rearth, and density=8.8 +/- 2.9 gcc. Kepler-10b is the smallest transiting exoplanet discovered to date.