Light-harvesting components of photosynthetic organisms are complex, coupled, many-body quantum systems, in which electronic coherence has recently been shown to survive for relatively long timescales, despite the decohering effects of their environments. Here, we analyse entanglement in multichromophoric light-harvesting complexes, and establish methods for quantification of entanglement by describing necessary and sufficient conditions for entanglement and by deriving a measure of global entanglement. These methods are then applied to the Fenna-Matthews-Olson protein to extract the initial state and temperature dependencies of entanglement. We show that, although the Fenna-Matthews-Olson protein in natural conditions largely contains bipartite entanglement between dimerized chromophores, a small amount of long-range and multipartite entanglement should exist even at physiological temperatures. This constitutes the first rigorous quantification of entanglement in a biological system. Finally, we discuss the practical use of entanglement in densely packed molecular aggregates such as light-harvesting complexes.