This article examined the suitability of CuI as a high performance p-type transparent conductor. Using sophisticated charge transport modelling, an upper limit to hole mobility as a function of carrier concentration was predicted, ranging from 162 cm 2 V -1 s -1 in the phonon-limited range to 32.6 cm 2 V -1 s -1 in the degenerately doped, ionised impurity-limited range. These results suggest significant scope for improvement in experimental mobility, particularly in the low to mid-concentration range, which could be achieved by mitigating surface and grain boundary scattering processes, and by further optimisation of synthesis conditions. An examination of the defect chemistry revealed that the copper vacancy is the predominant source of charge carriers in CuI, and that modulation of the copper chemical potential during synthesis is key to controlling hole concentration. The chalcogens S and Se are predicted to be electronically benign dopants, but can result in increased conductivity and hole concentration via indirect effects such as improved sample crystallinity. This work will act as a useful benchmark to experimental studies on CuI and related p-type transparent conductors, and indicates that there is still scope for enhanced opto-electronic performance.