We present a 200 ks Chandra ACIS-I image of Cygnus A, and discuss a long linear feature seen in its counterlobe. This feature has a non-thermal spectrum and lies on the line connecting the brighter hotspot on the approaching side and the nucleus. We therefore conclude that this feature is (or was) a jet. However, the outer part of this X-ray jet does not trace the current counterjet observed in radio. No X-ray counterpart is observed on the jet side. Using light-travel time effects we conclude that this X-ray 50 kpc linear feature is a relic jet that contains enough low-energy plasma (gamma ~ 10^3) to inverse-Compton scatter cosmic microwave background photons, producing emission in the X-rays.