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<jats:title>ABSTRACT</jats:title> <jats:p>The direct study of molecular gas in inner protoplanetary disks is complicated by uncertainties in the spatial distribution of the gas, the time variability of the source, and the comparison of observations across a wide range of wavelengths. Some of these challenges can be mitigated with far-ultraviolet spectroscopy. Using new observations obtained with the <jats:italic>Hubble Space Telescope</jats:italic> Cosmic Origins Spectrograph, we measure column densities and rovibrational temperatures for CO and H<jats:sub>2</jats:sub> observed on the line of sight through the AA Tauri circumstellar disk. CO <jats:italic>A</jats:italic> – <jats:italic>X</jats:italic> absorption bands are observed against the far-UV continuum. The CO absorption is characterized by log<jats:sub>10</jats:sub>(<jats:italic>N</jats:italic>(<jats:sup>12</jats:sup>CO)) = 17.5 ± 0.5 cm<jats:sup>−2</jats:sup> and <jats:italic>T</jats:italic> <jats:sub>rot</jats:sub>(CO) = 500<jats:sup>+500</jats:sup> <jats:sub>−200</jats:sub> K, although this rotational temperature may underestimate the local kinetic temperature of the CO-bearing gas. We also detect <jats:sup>13</jats:sup>CO in absorption with an isotopic ratio of ∼20. We do not observe H<jats:sub>2</jats:sub> absorption against the continuum; however, hot H<jats:sub>2</jats:sub> (<jats:italic>v</jats:italic> &gt; 0) is detected in absorption against the Lyα emission line. We measure the column densities in eight individual rovibrational states, determining a total log<jats:sub>10</jats:sub>(<jats:italic>N</jats:italic>(H<jats:sub>2</jats:sub>)) = 17.9<jats:sup>+0.6</jats:sup> <jats:sub>−0.3</jats:sub> cm<jats:sup>−2</jats:sup> with a thermal temperature of <jats:italic>T</jats:italic>(H<jats:sub>2</jats:sub>) = 2500<jats:sup>+800</jats:sup> <jats:sub>−700</jats:sub> K. The high temperature of the molecules, the relatively small H<jats:sub>2</jats:sub> column density, and the high inclination of the AA Tauri disk suggest that the absorbing gas resides in an inner disk atmosphere. If the H<jats:sub>2</jats:sub> and CO are cospatial within a molecular layer ∼0.6 AU thick, this region is characterized by <jats:inline-formula> <jats:tex-math /> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apj406368ieqn1.gif" xlink:type="simple" /> </jats:inline-formula> ∼ 10<jats:sup>5</jats:sup> cm<jats:sup>−3</jats:sup> with an observed 〈CO/H<jats:sub>2</jats:sub>〉 ratio of ∼0.4. We also find evidence for a departure from a purely thermal H<jats:sub>2</jats:sub> distribution, suggesting that excitation by continuum photons and H<jats:sub>2</jats:sub> formation may be altering the level populations in the molecular gas.</jats:p>