By adapting the concept of epitaxy to two-dimensional space, we show the growth of a single-atomic-layer, in-plane heterostructure of a prototypical material system-graphene and hexagonal boron nitride (h-BN). Monolayer crystalline h-BN grew from fresh edges of monolayer graphene with atomic lattice coherence, forming an abrupt one-dimensional interface, or boundary. More important, the h-BN lattice orientation is solely determined by the graphene, forgoing configurations favored by the supporting copper substrate.