We present a spectral analysis of the UV-bright star vZ 1128 in M3 based on observations with the Far Ultraviolet Spectroscopic Explorer (FUSE), the Space Telescope Imaging Spectrograph (STIS), and the Keck HIRES echelle spectrograph. By fitting the H I, He I, and He II lines in the Keck spectrum with non-LTE H-He models, we obtain Teff = 36,600 K, log g = 3.95, and log N(He)/N(H) = -0.84. The star's FUSE and STIS spectra show photospheric absorption from C, N, O, Al, Si, P, S, Fe, and Ni. No stellar features from elements beyond the iron peak are observed. Both components of the N V 1240 doublet exhibit P~Cygni profiles, indicating a weak stellar wind, but no other wind features are seen. The star's photospheric abundances appear to have changed little since it left the red giant branch (RGB). Its C, N, O, Al, Si, Fe, and Ni abundances are consistent with published values for the red-giant stars in M3, and the relative abundances of C, N, and O follow the trends seen on the cluster RGB. In particular, its low C abundance suggests that the star left the asymptotic giant branch before the onset of third dredge-up. ; Comment: 15 pages, 10 figures, to be published in MNRAS