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We present the first reliable determination of chemical abundances in an active galactic nucleus (AGN) outflow. The abundances are extracted from the deep and simultaneous Far Ultraviolet Spectroscopic Explorer (FUSE) and Hubble Space Telescope (HST ) STIS observations of Mrk 279. This data set is exceptional for its high signal-to-noise ratio, unblended doublet troughs, and little Galactic absorption contamination. These attributes allow us to solve for the velocity-dependent covering fraction and therefore obtain reliable column densities for many ionic species. For the first time, we have enough such column densities to simultaneously determine the ionization equilibrium and abundances in the flow. Our analysis uses the full spectral information embedded in these high-resolution data. Slicing a given trough into many independent outflow elements yields the extra constraints needed for a physically meaningful abundance determination. We find that relative to solar, the abundances in the Mrk 279 outflow are (linear scaling) carbon 2.2 ± 0.7, nitrogen 3.5 ± 1.1, and oxygen 1.6 ± 0.8. Our UV-based photoionization and abundance results are in good agreement with the independent analysis of the simultaneous Mrk 279 X-ray spectra. This is the best agreement between the UV and X-ray analyses of the same outflow to date.