Tropical ozone variability is analysed in a version of the Met Office Unified Model with stratospheric chemistry and transport. The model reproduced the stratospheric quasi-biennial oscillation (QBO) in the equatorial winds, forced by a broad spectrum of atmospheric waves. This resulted in a corresponding ozone QBO with vertical phase reversal near 10 hPa and amplitude consistent with observations. It was driven mainly by the QBO-induced vertical velocity anomaly, with the 10 hPa phase reversal a consequence of the sign change in the mean ozone vertical gradient. Chemistry was important for determining phase differences between the ozone and dynamical QBOs. Simulated column ozone anomalies were in reasonable agreement with observations in the tropics, but too weak in the sub-tropics. Nonetheless, the observed sub-tropical to tropical phase reversal and seasonal synchronization of the sub-tropical anomalies were reproduced. In contrast to some other studies our ozone QBO was obtained without QBO-induced variations in NOy transport, implying that ozone transport is an important forcing term in the upper, as well as the lower, stratosphere. In the lower stratosphere (21.5 hPa), diabatic effects of the ozone QBO increased the amplitude of the temperature oscillation by 35%. The mean period of the wind oscillation was also extended by about 10%, due to a longer westerly phase. These results imply that a better representation of chemical, as well as dynamical processes, will be required for improving the inter-annual variability in the tropical stratosphere in climate models.