We present recent Chandra X-ray observations of the RX J0821.0+0752 galaxy cluster, in addition to ALMA observations of the CO(1-0) and CO(3-2) line emission tracing the molecular gas in its central galaxy. All of the CO line emission, originating from a molecular gas reservoir, is located several kiloparsecs away from the nucleus of the central galaxy. The cold gas is concentrated into two main clumps surrounded by a diffuse envelope. They form a wide filament coincident with a plume of bright X-ray emission emanating from the cluster core. This plume encompasses a putative X-ray cavity that is only large enough to have uplifted a small percent of the molecular gas. Unlike other brightest cluster galaxies, stimulated cooling, where X-ray cavities lift low-entropy cluster gas until it becomes thermally unstable, cannot have produced the observed gas reservoir. Instead, the molecular gas has likely formed as a result of sloshing motions in the intracluster medium induced by a nearby galaxy. Sloshing can emulate uplift by dislodging gas from the galactic center. This gas has the shortest cooling time, so it will condense if disrupted for long enough.