We present high angular resolution X-ray images and spectra from two Chandra AXAF CCD Imaging Spectrometer (ACIS-I) observations of the X-ray jet in the nearby radio galaxy Cen A. We find that the X-ray emission from the jet is composed of a low surface brightness diffuse component extending continuously from within at least 60 pc of the active nucleus into the northeast radio lobe 4 kpc from the nucleus, along with 31 discrete compact knots, most of which are extended at the resolution of our observation. We find that there are small but significant differences between the X-ray and radio morphologies of the inner jet at the arcsecond level, making it unlikely that a single, spatially coincident population of ultrarelativistic electrons is responsible for the emission in both energy regimes. We suggest that the X-ray knots of the inner jet are indeed the sites of particle acceleration and shocks and that the X-ray and radio knot offsets are caused by a combination of particle diffusion and energy loss. These offsets may be a common feature of all jets in radio galaxies, or at least jets in FR I galaxies, and may be fundamental to the physics of such jets. They are best observed in Cen A because the source is so close. Even though the X-ray and radio knots are offset in position and there are variations of more than a factor of 3 in the ratio of X-ray to radio flux density in the inner jet, the radio to X-ray two-point spectral indices at the X-ray knots are not unusually flat and are consistent with those observed in other X-ray jets seen in FR I galaxies such as M87 and 3C 66B. We find the width of the jet in the X-ray bandpass to be narrower than that measured in the radio along most of its length. The X-ray spectra of several regions of the jet are well fitted by absorbed power-law models with photon indices � 2.2– 2.5, although the spectrum of one bright knot located � 1 kpc from the nucleus (knot B) is harder (photon index = 2.0). Subject headings: galaxies: active — galaxies: individual (Centaurus A, NGC 5128) — galaxies: jets — X-rays: galaxies