The Kepler Mission has recently announced the discovery of Kepler-10 b , the smallest exoplanet discovered to date and the first rocky planet found by the spacecraft . A second , 45-day period transit-like signal present in the photometry from the first eight months of data could not be confirmed as being caused by a planet at the time of that announcement . Here we apply the light-curve modeling technique known as BLENDER to explore the possibility that the signal might be due to an astrophysical false positive ( blend ) . To aid in this analysis we report the observation of two transits with the Spitzer Space Telescope at 4.5 µm . When combined they yield a transit depth of 344 \pm 85 ppm that is consistent with the depth in the Kepler passband ( 376 \pm 9 ppm , ignoring limb darkening ) , which rules out blends with an eclipsing binary of a significantly different color than the target . Using these observations along with other constraints from high-resolution imaging and spectroscopy we are able to exclude the vast majority of possible false positives . We assess the likelihood of the remaining blends , and arrive conservatively at a false alarm rate of 1.6 \times 10 ^ { -5 } that is small enough to validate the candidate as a planet ( designated Kepler-10 c ) with a very high level of confidence . The radius of this object is measured to be R _ { p } = 2.227 _ { -0.057 } ^ { +0.052 } R _ { \earth } ( in which the error includes the uncertainty in the stellar properties ) , but currently available radial-velocity measurements only place an upper limit on its mass of about 20 M _ { \earth } . Kepler-10 c represents another example ( with Kepler-9 d and Kepler-11 g ) of statistical “ validation ” of a transiting exoplanet , as opposed to the usual “ confirmation ” that can take place when the Doppler signal is detected or transit timing variations are measured . It is anticipated that many of Kepler ’ s smaller candidates will receive a similar treatment since dynamical confirmation may be difficult or impractical with the sensitivity of current instrumentation .