The jet in 3C 273 is a high-power quasar jet with radio, optical, and X-ray emission, whose size and brightness allow a detailed study of the emission processes acting in it. We present deep Chandra observations of this jet and analyze the spectral properties of the jet emission from radio through X-rays. We find that the X-ray spectra are significantly softer than the radio spectra in all regions of the bright part of the jet, except for the first bright ''knot A,'' ruling out a model in which the X-ray emission from the entire jet arises from beamed inverse Compton scattering of cosmic microwave background photons in a single-zone jet flow. Within two-zone jet models, we find that a synchrotron origin for the jet's X-rays requires fewer additional assumptions than an inverse Compton model, especially if velocity shear leads to efficient particle acceleration in jet flows.