Far-ultraviolet spectra were obtained of the active cool star AB Doradus (HD 36705) during the calibration and checkout period of the Far Ultraviolet Spectroscopic Explorer (FUSE) satellite. Observations in this early phase of the mission were taken at a resolving power of 12,000-15,000 (~20-25 km s-1) and covered the spectral range 905-1187 Å. The integrated spectrum exhibits strong, rotationally broadened stellar emission from C III (λλ977, 1175) and O VI (λλ1032, 1037) and many weaker lines. Strong emission lines of C III and O VI exhibit broad wings. The C III λ977 profile shows blueshifted absorption at ~30 km s-1, and C II λ1036 absorption appears superposed on emission in the wing of O VI λ1037. Rotational modulation of C III and O VI is present, in harmony with its photometric variability. Flares were detected in the brightest lines, and subexposures were analyzed to examine flux and profile variations. Downflows that extend to 600 km s-1 during a flare are found in the O VI profiles. These early observations demonstrate that FUSE will be an exceptional instrument for studying chromospheres in cool stars.