Ventilation of adjacent, connected chambers, forced in one chamber by an isolated point source of buoyancy is investigated. There are floor- and ceiling-level external openings in the forced and unforced chambers, respectively, while the partition between the chambers has both a floor- and ceiling-level opening. The flow evolves on the time scale over which the volume flux associated with the plume at the ceiling would fill both chambers. The steady state in the forced chamber is analogous to the single chamber flow described by Linden, Lane-Serff & Smeed (J. Fluid Mech., vol. 212, 1990, p. 309), with a well-mixed buoyant upper layer which is deeper than in the single chamber flow due to the extra pressure drop at the upper interior opening. The steady state in the unforced chamber inevitably exhibits vertical stratification, and depends on the transient flow, all the opening areas, and the relative plan area of the two chambers, as is verified by laboratory experiments. When the upper interior opening is relatively large, the buoyant layer in the unforced chamber is deeper than the buoyant layer in the forced chamber, which contradicts model predictions based on the assumption that the layers are always well-mixed.