The phycobilisome is the primary light-harvesting antenna in cyanobacterial and red algal oxygenic photosynthesis. It maintains near-unity efficiency of energy transfer to reaction centers despite relying on slow exciton hopping along a relatively sparse network of highly fluorescent phycobilin chromophores. How the complex maintains this high efficiency remains unexplained. Using a two-dimensional electronic spectroscopy polarization scheme that enhances energy transfer features, we directly watch energy flow in the phycobilisome complex of Synechocystis sp. PCC 6803 from the outer phycocyanin rods to the allophycocyanin core. The observed downhill flow of energy, previously hidden within congested spectra, is faster than timescales predicted by Förster hopping along single rod chromophores. We attribute the fast, 8 ps energy transfer to interactions between rod-core linker proteins and terminal rod chromophores, which facilitate unidirectionally downhill energy flow to the core. This mechanism drives the high energy transfer efficiency in the phycobilisome and suggests that linker protein-chromophore interactions have likely evolved to shape its energetic landscape.