The Chandra Multiwavelength Project (ChaMP) has discovered a jet-like structure associated with a newly recognized QSO at redshift z=1.866. The system was 9.4 arcmin off-axis during an observation of 3C 207. Although significantly distorted by the mirror PSF, we use both a raytrace and a nearby bright point source to show that the X-ray image must arise from some combination of point and extended sources, or else from a minimum of three distinct point sources. We favor the former situation, as three unrelated sources would have a small probability of occurring by chance in such a close alignment. We show that interpretation as a jet emitting X-rays via inverse Compton (IC) scattering on the cosmic microwave background (CMB) is plausible. This would be a surprising and unique discovery of a radio-quiet QSO with an X-ray jet, since we have obtained upper limits of 100 microJy on the QSO emission at 8.46 GHz, and limits of 200 microJy for emission from the putative jet.