We report the detection of an optical jet in the nearby Seyfert 1 radio galaxy 3C 120. The optical jet coincides with the well-known radio jet and emits continuum radiation (B, V', I) with a radio-to-optical spectral index of 0.65. There are no clear optical counterparts to the radio knots, although the optical condensation A of the galaxy, which includes the bright 4'' radio knot, is found to be 12% polarized with the electric field vectors perpendicular to the jet. These findings indicate that 3C 120 contains the sixth known extragalactic optical synchrotron jet, quite similar in its properties to the jet of PKS 0521-36. The outer part of the jet is the faintest known optical jet and was discovered as the result of a dedicated effort to detect it. It is therefore possible that more optical jets can be discovered in systematic searches by combining deep imaging in the optical or near-infrared with careful galaxy subtraction methods.