  The relative abundances of atomic and molecular species in planet-forming
disks around young stars provide important constraints on photochemical disk
models and provide a baseline for calculating disk masses from measurements of
trace species. A knowledge of absolute abundances, those relative to molecular
hydrogen (H2), are challenging because of the weak rovibrational transition
ladder of H$_{2}$ and the inability to spatially resolve different emission
components within the circumstellar environment. To address both of these
issues, we present new contemporaneous measurements of CO and H2 absorption
through the "warm molecular layer" of the protoplanetary disk around the
Classical T Tauri Star RW Aurigae A. We use a newly commissioned observing mode
of the Hubble Space Telescope-Cosmic Origins Spectrograph to detect warm H2
absorption in this region for the first time. An analysis of the emission and
absorption spectrum of RW Aur shows components from the accretion region near
the stellar photosphere, the molecular disk, and several outflow components.
The warm H2 and CO absorption lines are consistent with a disk origin. We model
the 1092-1117A spectrum of RW Aur to derive log10
N(H2)~=~19.90$^{+0.33}_{-0.22}$ at T$_{rot}$(H2) ~=~440~+/-~39 K. The CO
$A$~--~$X$ bands observed from 1410-1520A are best fit by log10
N(CO)~=~16.1~$^{+0.3}_{-0.5}$ at T$_{rot}$(CO) ~=~200$^{+650}_{-125}$ K.
Combining direct measurements of the HI, H2, and CO column densities, we find a
molecular fraction in the warm disk surface of $f_{H2}$~>=~0.47 and derive a
molecular abundance ratio of CO/H2~=~1.6$^{+4.7}_{-1.3}$~x~10$^{-4}$, both
consistent with canonical interstellar dense cloud values.
