The modestly eccentric and non-coplanar orbits of the giant planets pose a challenge to solar system formation theories which generally indicate that the giant planets emerged from the protoplanetary disk in nearly perfectly circular and coplanar orbits. We demonstrate that a single encounter with a 2-50 Jupiter-mass object, passing through the solar system at a perihelion distance less than 20 AU and a hyperbolic excess velocity of 1-3 km/s, can excite the giant planets' eccentricities and mutual inclinations to values comparable to those observed. We describe a metric to evaluate how closely a simulated flyby system matches the eccentricity and inclination secular modes of the solar system. We estimate that there is about a 1-in-9000 chance that such a flyby occurs during the solar system's residence in its primordial cluster and produces a dynamical architecture similar to that of the solar system. The scenario of an ancient close encounter with a substellar object offers a plausible explanation for the origin of the moderate eccentricities and inclinations and the secular architecture of the planets. We discuss some broader implications of disruptive flyby encounters on planetary systems in the Galaxy.