KIC 7177553 was observed by the Kepler satellite to be an eclipsing eccentric binary star system with an 18-day orbital period. Recently, an eclipse timing study of the Kepler binaries has revealed eclipse timing variations in this object with an amplitude of about 100 sec, and an outer period of 529 days. The implied mass of the third body is that of a superJupiter, but below the mass of a brown dwarf. We therefore embarked on a radial velocity study of this binary to determine its system configuration and to check the hypothesis that it hosts a giant planet. From the radial velocity measurements, it became immediately obvious that the same Kepler target contains another eccentric binary, this one with a 16.5-day orbital period. Direct imaging using adaptive optics reveals that the two binaries are separated by 0.4 arcsec (about 167 AU), and have nearly the same magnitude (to within 2%). The close angular proximity of the two binaries, and very similar Gamma velocities, strongly suggest that KIC 7177553 is one of the rare SB4 systems consisting of two eccentric binaries where at least one system is eclipsing. Both systems consist of slowly rotating, non-evolved, solar-like stars of comparable masses. From the orbital separation and the small difference in Gamma velocity, we infer that the period of the outer orbit most likely lies in the range 1000 to 3000 years. New images taken over the next few years, as well as the high-precision astrometry of the Gaia satellite mission, will allow us to set much narrower constraints on the system geometry. Finally, we note that the observed eclipse timing variations in the Kepler data cannot be produced by the second binary. Further spectroscopic observations on a longer time scale will be required to prove the existence of the massive planet.