Computed tomography of a chemiluminescence (CTC) system was implemented to provide time-resolved 3D measurements of an unconfined turbulent swirl flame. This system was designed in a cost-effective manner and employed three customized view registration assemblies to simultaneously capture eight projections of the target flame at a repetition rate of 4 kHz. Both time-resolved and time-averaged tomographic reconstructions were performed based on data acquired for a duration of 250 ms. Both qualitative and quantitative validations suggested the correctness of our implementation. The time-resolved instantaneous reconstructions successfully captured the evolution of the structural features of the swirl flame such as local extinctions and the helical mode. Based on the reconstructions, the centroids of chemiluminescence for all the layers were calculated. The trajectory of these centroids provided insights into the flow motion and suggested a rotating helical structure of the swirl flame. These results demonstrated the feasibility of resolving the dynamics of turbulent swirl flames with a kHz temporal resolution using the relatively inexpensive CTC system.