The near-unity efficiency of energy transfer in photosynthesis makes photosynthetic light-harvesting complexes a promising avenue for developing new renewable energy technologies. Knowledge of the energy landscape of these complexes is essential in understanding their function, but its experimental determination has proven elusive. Here, the observation of quantum coherence using two-dimensional electronic spectroscopy is employed to directly measure the 14 lowest electronic energy levels in light-harvesting complex II (LHCII), the most abundant antenna complex in plants containing approximately 50% of the world's chlorophyll. We observe that the electronically excited states are relatively evenly distributed, highlighting an important design principle of photosynthetic complexes that explains the observed ultrafast intracomplex energy transfer in LHCII.