We have analyzed the UV photospheric lines of Plaskett's star (HD 47129), a 14.4 day period, double-lined O-type spectroscopic binary. Archival data from IUE (17 spectra well distributed in orbital phase) were analyzed with several techniques. A cross-correlation analysis, which showed that the secondary produces significant lines in the UV, indicates that the mass ratio is q = 1.18 +/- 0.12 (secondary slightly more massive). A tomography algorithm was used to produce the separate spectra of the two stars in six spectral regions. The MK spectral classifications of the primary and secondary, O7.5 I and O6 I, respectively, were estimated through a comparison of UV line ratios with those in spectral standard stars. The intensity ratio of the stars in the UV is 0.53 +/- 0.05 (primary brighter). The secondary has a strong P Cygni N IV lambda-1718 feature, indicating a strong stellar wind. The secondary lines appear rotationally broadened, and we estimate the projected rotational velocity V sin i for this star to be 310 +/- 20 km s-1. We discuss the possible evolutionary history of this system through a comparison of the positions of the components and evolutionary tracks in the H-R diagram.