We present the first time-dependent density functional theory (TDDFT) calculation on a light-harvesting triad carotenoid-diaryl-porphyrin-C-60. Besides the numerical challenge that the ab initio study of the electronic structure of such a large system presents, we show that TDDFT is able to provide an accurate description of the excited-state properties of the system. In particular, we calculate the photoabsorption spectrum of the supramolecular assembly, and we provide an interpretation of the photoexcitation mechanism in terms of the properties of the component moieties. The spectrum is in good agreement with experimental data, and provides useful insight on the photoinduced charge-transfer mechanism which characterizes the system.