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We report the discovery of a transiting, Rp = 4.347+/-0.099REarth,circumbinary planet (CBP) orbiting the Kepler K+M Eclipsing Binary (EB) systemKIC 12351927 (Kepler-413) every ~66 days on an eccentric orbit with ap =0.355+/-0.002AU, ep = 0.118+/-0.002. The two stars, with MA =0.820+/-0.015MSun, RA = 0.776+/-0.009RSun and MB = 0.542+/-0.008MSun, RB =0.484+/-0.024RSun respectively revolve around each other every10.11615+/-0.00001 days on a nearly circular (eEB = 0.037+/-0.002) orbit. Theorbital plane of the EB is slightly inclined to the line of sight (iEB =87.33+/-0.06 degrees) while that of the planet is inclined by ~2.5 degrees tothe binary plane at the reference epoch. Orbital precession with a period of~11 years causes the inclination of the latter to the sky plane to continuouslychange. As a result, the planet often fails to transit the primary star atinferior conjunction, causing stretches of hundreds of days with no transits(corresponding to multiple planetary orbital periods). We predict that the nexttransit will not occur until 2020. The orbital configuration of the systemplaces the planet slightly closer to its host stars than the inner edge of theextended habitable zone. Additionally, the orbital configuration of the systemis such that the CBP may experience Cassini-States dynamics under the influenceof the EB, in which the planet's obliquity precesses with a rate comparable toits orbital precession. Depending on the angular precession frequency of theCBP, it could potentially undergo obliquity fluctuations of dozens of degrees(and complex seasonal cycles) on precession timescales.

Kepler-413b: a slightly misaligned, Neptune-size transiting circumbinary planet