We present a Hubble Space Telescope image of the FR II radio galaxy 3C 401, obtained at 1.6 m with NICMOS, in which we identify the infrared counterpart of the brightest region of the radio jet. The jet has a complex radio structure and brightens where bending occurs, most likely as a result of relativistic beaming. We analyze archival data in the radio, optical, and X-ray bands, and we derive its spectral energy distribution. Unlike all of the previously known optical extragalactic jets, the jet in 3C 401 is not detected in the X-rays, even in a long 48 ks X-ray Chandra exposure, and the infrared emission dominates the overall spectral energy distribution (SED). We propose that the dominant radiation mechanism of this jet is synchrotron. The low X-ray emission is then caused by two different effects: (1) the lack of any strong external photon field and (2) the shape of the electron distribution. This affects the location of the synchrotron peak in the SED, resulting in a sharp cutoff at energies lower than the X-rays. Thus 3C 401 shows a new type of jet, with intermediate spectral properties between those of FR I galaxies, which are dominated by synchrotron emission up to X-ray energies, and FR II galaxies/QSOs, which show strong highenergy emission due to inverse Compton scattering of external photons. This might indicate the presence of a continuous ''sequence'' in the properties of large-scale jets, analogous to the ''blazar sequence'' already proposed for subparsec-scale jets.