Early time-series photometry from NASAs Kepler spacecraft has revealed a planet transiting the star we term Kepler-4, at RA = 19h02m27.68s, Dec = +50:08:08.7. The planet has an orbital period of 3.213 days and shows transits with a relative depth of 0.87 x 10^{-3} and a duration of about 3.95 hours. Radial velocity measurements from the Keck HIRES spectrograph show a reflex Doppler signal of 9.3 (+1.1 -1.9) m/s, consistent with a low-eccentricity orbit with the phase expected from the transits. Various tests show no evidence for any companion star near enough to affect the light curve or the radial velocities for this system. From a transit-based estimate of the host stars mean density, combined with analysis of high-resolution spectra, we infer that the host star is near turnoff from the main sequence, with estimated mass and radius of 1.223 (+0.053 -0.091) solar masses and 1.487 (+0.071 -0.084) solar radii. We estimate the planet mass and radius to be 24.5 +/- 3.8 Earth masses and 3.99 +/- 0.21 Earth radii. The planets density is near 1.9 g/cm^3; it is thus slightly denser and more massive than Neptune, but about the same size.
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