  Saturn's largest satellite, Titan, transited the Crab Nebula on 5 January
2003. We observed this astronomical event with the {\it Chandra} X-ray
Observatory. An ``occultation shadow'' has clearly been detected and is found
to be larger than the diameter of Titan's solid surface. The difference gives a
thickness for Titan's atmosphere of 880 $\pm$ 60 km. This is the first
measurement of Titan's atmospheric extent at X-ray wavelengths. The value
measured is consistent with or slightly larger than those estimated from
earlier Voyager observations at other wavelengths. We discuss the possibility
of temporal variations in the thickness of Titan's atmosphere.
