We present the first results from an X-ray and optical survey of a sample of radio jets in active galactic nuclei with Chandra and the Hubble Space Telescope (HST). We focus here on the first six sources observed in X-ray, in four of which a bright X-ray jet was detected for the first time. In three out of the four cases, optical emission from the jet is also detected in our HST images. We compare the X-ray morphology with the radio as derived from improved processing of archival Very Large Array data, and we construct spectral energy distributions (SEDs) for the most conspicuous emission knots. In most cases, the SEDs, together with the similarity of the X-ray and radio morphologies, favor an inverse Compton origin for the X-rays. The most likely origin of the seed photons is the cosmic microwave background, implying the jets are still relativistic on kiloparsec scales. However, in the first knot of the PKS 1136-135 jet, X-rays are likely produced via the synchrotron process. In all four cases, bulk Lorentz factors of a few are required. The radio maps of the two jets not detected by either Chandra or HST suggest that they are less beamed at large scales than the other four detected sources. Our results demonstrate that, at the sensitivity and resolution of Chandra, X-ray emission from extragalactic jets is common, yielding essential information on their physical properties.