In the first picoseconds of photosynthesis, photoexcitations of chlorophyll molecules are passed through a network of chlorophyll-binding proteins to a charge transfer site, initiating the conversion of absorbed energy to chemical fuels. The remarkably high quantum efficiency of this energy transfer relies on near-field coupling between adjacent chlorophyll molecules and their interaction with protein phonon modes. Using two-dimensional electronic spectroscopy, we track the time-evolution of energy flow in a chlorophyll-protein complex, CP29, found in green plants. The results from these nonlinear four-wave mixing experiments elucidate the role of CP29 as a light harvester and energy conduit by drawing causal relationships between the spatial and electronic configurations of its chlorophyll molecules. Through independent control of experimental light pulse polarizations, we have furthermore developed a technique to determine the relative angles between the transition dipole moments responsible for energy transfer. This work not only yields tools for structural and spectral molecular characterization, but also deepens our understanding of how photosynthetic systems have evolved to optimize the conversion of light to biomass.