We describe the hydrogen Lyalpha emission of the spectroscopic binary Capella (G8 III + GO III) recorded at 0.1 angstrom resolution by the International Ultraviolet Explorer. The overt changes in the composite line shape with orbital phase are controlled by the active GO III star and permit a dissection of the stellar components despite the obliteration of the central portion of the profile by atomic hydrogen and deuterium absorption along the 12.5 pc sightline. The Lyalpha line shape of the active GO III star is surprisingly asymmetric and possibly is variable. Both characteristics suggest a stellar wind of moderate excitation (2 x 10(4)-1 x 10(5) K), a key component of the coronal evolution scenario of Simon & Drake for the Hertzsprung-gap giants. In a companion paper Linsky et al. use the intrinsic Lyalpha line shape of Capella to derive the interstellar hydrogen column density and the cosmologically significant D/H ratio based on a comparison with a 0.015 angstrom resolution profile obtained by the Goddard High Resolution Spectrograph of the Hubble Space Telescope.