Observation shows that nebular emission, molecular gas, and young stars in giant galaxies are associated with rising X-ray bubbles inflated by radio jets launched from nuclear black holes. We propose a model where molecular clouds condense from low-entropy gas caught in the updraft of rising X-ray bubbles. The low-entropy gas becomes thermally unstable when it is lifted to an altitude where its cooling time is shorter than the time required to fall to its equilibrium location in the galaxy, i.e., $t$/$\textit{t}$1 $\lesssim$1. The infall speed of a cloud is bounded by the lesser of its free-fall and terminal speeds, so that the infall time here can exceed the free-fall time by a significant factor. This mechanism is motivated by Atacama Large Millimeter Array observations revealing molecular clouds lying in the wakes of rising X-ray bubbles with velocities well below their free-fall speeds. Our mechanism would provide cold gas needed to fuel a feedback loop while stabilizing the atmosphere on larger scales. The observed cooling time threshold of $\sim$5x10$^{8}$ yr—the clear-cut signature of thermal instability and the onset of nebular emission and star formation—may result from the limited ability of radio bubbles to lift low-entropy gas to altitudes where thermal instabilities can ensue. Outflowing molecular clouds are unlikely to escape, but instead return to the central galaxy in a circulating flow. We contrast our mechanism to precipitation models where the minimum value of $t$/$t$ $\lesssim$10 triggers thermal instability, which we find to be inconsistent with observation.