Our Chandra observation of the FR I radio galaxy 3C 66B has resulted in the first detection of an X-ray counterpart to the previously known radio, infrared and optical jet. The X-ray jet is detected up to 7arcsec from the core and has a steep X-ray spectrum, α~1.3±0.1. The overall X-ray flux density and spectrum of the jet are consistent with a synchrotron origin for the X-ray emission. However, the inner knot in the jet has a higher ratio of X-ray to radio emission than the others. This suggests that either two distinct emission processes are present or differences in the acceleration mechanism are required; there may be a contribution to the emission from the inner knot from an inverse Compton process or it may be the site of an early strong shock in the jet. The peak of the brightest radio and X-ray knot is significantly closer to the nucleus in the X-ray than in the radio, which may suggest that the knots are privileged sites for high-energy particle acceleration. 3C 66B's jet is similar both in overall spectral shape and in structural detail to those in more nearby sources such as M87 and Centaurus A.