We describe the first results from a six-month long reverberation-mapping experiment in the ultraviolet based on 171 observations of the Seyfert 1 galaxy NGC 5548 with the Cosmic Origins Spectrograph on the Hubble Space Telescope. Significant correlated variability is found in the continuum and broad emission lines, with amplitudes ranging from ~30% to a factor of two in the emission lines and a factor of three in the continuum. The variations of all the strong emission lines lag behind those of the continuum, with He ii $\lambda 1640$ lagging behind the continuum by ~2.5 days and Lyα $\lambda 1215$, C iv $\lambda 1550$, and Si iv $\lambda 1400$ lagging by ~5–6 days. The relationship between the continuum and emission lines is complex. In particular, during the second half of the campaign, all emission-line lags increased by a factor of 1.3–2 and differences appear in the detailed structure of the continuum and emission-line light curves. Velocity-resolved cross-correlation analysis shows coherent structure in lag versus line of sight velocity for the emission lines; the high-velocity wings of C iv respond to continuum variations more rapidly than the line core, probably indicating higher velocity broad-line region clouds at smaller distances from the central engine. The velocity-dependent response of Lyα, however, is more complex and will require further analysis.