In photosynthesis, solar energy capture to conversion occurs with a remarkable near-unity quantum efficiency through energy transport across a network of chromophore-containing proteins. Thermal fluctuations of these proteins lead to changes in the intermolecular interactions that drive energy transport. Despite this variation, high efficiency of transport is maintained. Both the extent to which the dynamics of energy transport vary and how the efficiency is robust to variation remain unclear. Previous measurements either lacked the temporal resolution required or the sensitivity to measure individual proteins, and thus averaged over the fluctuations. Here, we describe a new experiment, single-molecule pump-probe (SM2P) spectroscopy, that measures excited-state dynamics with femtosecond time resolution in single proteins. We demonstrate the power of this technique on cyanobacterial light-harvesting subunits. Our experiments reveal heterogeneous timescales of vibrational relaxation, yet a narrow distribution of energy transfer timescales. These results suggest the protein design serves to tightly regulate energy transfer despite fluctuations of its structure.