The dominant form of oxygen in cold molecular clouds is gas-phase carbon monoxide (CO) and ice-phase water (H2O). Yet, in planet-forming disks around young stars, gas-phase CO and H2O are less abundant relative to their interstellar medium values, and no other major oxygen-carrying molecules have been detected. Some astrochemical models predict that gas-phase molecular oxygen (O2) should be a major carrier of volatile oxygen in disks. We report a deep search for emission from the isotopologue 16O18O (N J = 21 − 01 line at 233.946 GHz) in the nearby protoplanetary disk around TW Hya. We used imaging techniques and matched filtering to search for weak emission but do not detect 16O18O. Based on our results, we calculate upper limits on the gas-phase O2 abundance in TW Hya of (6.4–70) × 10−7 relative to H, which is 2–3 orders of magnitude below solar oxygen abundance. We conclude that gas-phase O2 is not a major oxygen carrier in TW Hya. Two other potential oxygen-carrying molecules, SO and SO2, were covered in our observations, which we also do not detect. Additionally, we report a serendipitous detection of the C15N N J = 25/2 − 13/2 hyperfine transitions, F = 3 − 2 and F = 2 − 1, at 219.9 GHz, which we found via matched filtering and confirm through imaging.