We present Kepler observations of the bright (V = 8.3), oscillating star HD 179070. The observations show transit-like events which reveal that the star is orbited every 2.8 days by a small, 1.6 R Earth object. Seismic studies of HD 179070 using short cadence Kepler observations show that HD 179070 has a frequency-power spectrum consistent with solar-like oscillations that are acoustic p-modes. Asteroseismic analysis provides robust values for the mass and radius of HD 179070, 1.34 ± 0.06 M &sun; and 1.86 ± 0.04 R &sun;, respectively, as well as yielding an age of 2.84 ± 0.34 Gyr for this F5 subgiant. Together with ground-based follow-up observations, analysis of the Kepler light curves and image data, and blend scenario models, we conservatively show at the >99.7% confidence level (3σ) that the transit event is caused by a 1.64 ± 0.04 R Earth exoplanet in a 2.785755 ± 0.000032 day orbit. The exoplanet is only 0.04 AU away from the star and our spectroscopic observations provide an upper limit to its mass of ~10 M Earth (2σ). HD 179070 is the brightest exoplanet host star yet discovered by Kepler. Based in part on observations obtained at the W. M. Keck Observatory, which is operated by the University of California and the California Institute of Technology, the Mayall telescope at Kitt Peak National Observatory, and the WIYN Observatory which is a joint facility of NOAO, University of Wisconsin-Madison, Indiana University, and Yale University.