Lithium intercalation into graphite is a critical process in energy storage technology. Studies of Li intercalation kinetics have proved challenging due to structural and phase complexity, and sample heterogeneity. Here we report direct time- and space-resolved, all-optical measurement of Li intercalation. We use a single crystal graphite electrode with lithographically defined disc geometry. All-optical, Raman and reflectance measurements distinguish the intrinsic intercalation process from side reactions, and provide new insight into the microscopic intercalation process. The recently proposed Cahn-Hilliard reaction (CHR) theory quantitatively captures the observed phase front spatial patterns and dynamics, using a two-layer free-energy model with novel, generalized Butler-Volmer kinetics. This approach unites Cahn-Hilliard and electrochemical kinetics, using a thermodynamically consistent description of the Li injection reaction at the crystal edge that involves a cooperative opening of graphene planes. The excellent agreement between experiment and theory presented here, with single-crystal resolution, provides strong support for the CHR theory of solid-state reactions.