We report the first detection of X-ray emission in a pre-planetary nebula, Hen 3-1475. Pre-planetary nebulae are rare objects in the short transition stage between the Asymptotic Giant Branch and planetary nebula evolutionary phases, and Hen 3-1475, characterised by a remarkable S-shaped chain of optical knots, is one of the most noteworthy members of this class. Observations with the Advanced CCD Imaging Spectrometer (ACIS) onboard the Chandra X-Ray observatory show the presence of compact emission coincident with the brightest optical knot in this bipolar object, which is displaced from the central star by 2.7 arcsec along the polar axis. Model fits to the X-ray spectrum indicate an X-ray temperature and luminosity, respectively, of (4.3-5.7) 10^6 K and (4+/-1.4) 10^{31} (D/5 kpc)^2 erg s^{-1}, respectively. Our 3-sigma upper limit on the luminosity of compact X-ray emission from the central star in Hen 3-1475 is ~5 10^{31} (D/5 kpc)^2 erg s^{-1}. The detection of X-rays in Hen 3-1475 is consistent with models in which fast collimated post-AGB outflows are crucial to the shaping of planetary nebulae; we discuss such models in the context of our observations.