Hotspot cooling is critical to the performance and reliability of electronic devices, but existing techniques are not very effective in managing mobile hotspots. We report a hotspot cooling technique based on a jumping-drop vapor chamber consisting of parallel plates of a superhydrophilic evaporator and a superhydrophobic condenser, where the working fluid is returned via the spontaneous out-of-plane jumping of condensate drops. While retaining the passive nature of traditional vapor-chamber heat spreaders (flat-plate heat pipes), the jumping-drop technique offers a mechanism to address mobile hotspots with a pathway toward effective thermal transport in the out-of-plane direction.