We present the first reliable determination of chemical abundances in an AGN outflow .
The abundances are extracted from the deep and simultaneous FUSE and HST/STIS observations of Mrk 279 .
This data set is exceptional for its high signal-to-noise , 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 abundances determination .
We find that relative to solar the abundances in the Mrk 279 outflow are ( linear scaling ) : carbon 2.2 \pm 0.7 , nitrogen 3.5 \pm 1.1 and oxygen 1.6 \pm 0.8 .
Our UV-based photoionization and abundances 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 .