The computed tomography of chemiluminescence (CTC) technique was applied for the first time to a real highly turbulent swirl flame setup, using a large number of CCD cameras (Nq=24 views), to directly reconstruct the three-dimensional instantaneous and time-averaged chemiluminescence fields. The views were obtained from a 172.5° region (in one plane) around the flame, and the CTC algorithm [Floyd et al., Combust. Flame158, 376 (2011)CBFMAO0010-2180] was used to reconstruct the flame by discretizing the domain into voxels. We investigated how the reconstructions are affected by the views' arrangement and the settings of the algorithm, and considered how the quality of reconstructions should be assessed to ensure a realistic description of the capabilities of the technique. Reconstructions using Nq≤12 were generally better when the cameras were distributed more equiangularly. When Nq was severely low (e.g., 3), the reconstruction could be improved by using fewer voxels. The paper concludes with a summary of the strengths and weaknesses of the CTC technique for examining a real turbulent flame geometry and provides guidance on best practice.