Of the nine confirmed transiting circumbinary planet systems, only Kepler-47 is known to contain more than one planet. Kepler-47 b (the inner planet) has an orbital period of 49.5 days and a radius of about $3,R_{oplus}$. Kepler-47 c (the outer planet) has an orbital period of 303.2 days and a radius of about $4.7,R_{oplus}$. Here we report the discovery of a third planet, Kepler-47 d (the middle planet), which has an orbital period of 187.4 days and a radius of about $7,R_{oplus}$. The presence of the middle planet allows us to place much better constraints on the masses of all three planets, where the $1sigma$ ranges are less than $26,M_{oplus}$, between $7-43,M_{oplus}$, and between $2-5,M_{oplus}$ for the inner, middle, and outer planets, respectively. The middle and outer planets have low bulk densities, with $rho_{rm middle} < 0.68$ g cm$^{-3}$ and $rho_{rm outer} < 0.26$ g cm$^{-3}$ at the $1sigma$ level. The two outer planets are tightly packed, assuming the nominal masses, meaning no other planet could stably orbit between them. All of the orbits have low eccentricities and are nearly coplanar, disfavoring violent scattering scenarios and suggesting gentle migration in the protoplanetary disk.
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