HAT-P-11 is a mid-K dwarf that hosts one of the first Neptune-sized planets found outside the solar system. The orbit of HAT-P-11b is misaligned with the star's spin - one of the few known cases of a misaligned planet orbiting a star less massive than the Sun. We find an additional planet in the system based on a decade of precision radial velocity (RV) measurements from Keck/High Resolution Echelle Spectrometer. HAT-P-11c is similar to Jupiter in its mass ( M J) and orbital period ( year), but has a much more eccentric orbit (e = 0.60 ± 0.03). In our joint modeling of RV and stellar activity, we found an activity-induced RV signal of ∼7 , consistent with other active K dwarfs, but significantly smaller than the 31 reflex motion due to HAT-P-11c. We investigated the dynamical coupling between HAT-P-11b and c as a possible explanation for HAT-P-11b's misaligned orbit, finding that planet-planet Kozai interactions cannot tilt planet b's orbit due to general relativistic precession; however, nodal precession operating on million year timescales is a viable mechanism to explain HAT-P-11b's high obliquity. This leaves open the question of why HAT-P-11c may have such a tilted orbit. At a distance of 38 pc, the HAT-P-11 system offers rich opportunities for further exoplanet characterization through astrometry and direct imaging.