Far Ultraviolet Spectroscopic Explorer FUSE observations of the bright binary system Capella (Alpha Aurigae; G1 III + G8 III) reveal a rich emission line spectrum containing neutral and ionic species, among them H I, O I, C III, O VI, S VI, Ne V and Ne VI. In addition the Fe XVIII 974.85 A line, formed at temperatures of approx. 6 x 10^6 K, is detected. Whereas the chromospheric and transition region emission is dominated by that from the G1 giant, consistent with results from previous ultraviolet observations, Fe XVIII is formed largely in the G8 giant atmosphere. Line ratios from C III suggest densities of 2-8 x 10^10 cm^-3, although anomalous line profiles of the 1176 transition may signal optical depth effects. The hydrogen Lyman series, detected for the first time, displays asymmetric emission consistent with an expanding atmosphere.