In December 2001, the Space Telescope Imaging Spectrograph of the Hubble Space Telescope obtained far-ultraviolet spectral images of Jupiter's moon Callisto. The leading and trailing hemispheres were observed in the spectral range 1190 Å to 1720 Å when the moon was at eastern and western elongations, respectively. We analyzed the hydrogen Lyman α (1216 Å) signal in the two observations and found that faint atmospheric emissions extending up to several moon radii away are present in addition to the solar flux reflected off the surface. We show that the detected atmospheric Lyman α emissions are consistent with an escaping hydrogen corona with a vertical column density in the range of (6-12) ×1011 cm-2. The derived hydrogen abundance is about 2 times higher when the moon is at eastern elongation, possibly related to increased water sublimation when the visibly darker leading hemisphere is illuminated by the Sun. The detected hemispheric difference is larger than the measurement uncertainties providing first evidence for variations in Callisto's neutral atmosphere.