If a bulk material can withstand a high load without any irreversible damage (such as plastic deformation), it is usually brittle and can fail catastrophically 1 , 2 . This trade-off between strength and fracture toughness also extends into two-dimensional materials space 3 , 4 , 5 . For example, graphene has ultrahigh intrinsic strength (about 130 gigapascals) and elastic modulus (approximately 1.0 terapascal) but is brittle, with low fracture toughness (about 4 megapascals per square-root metre) 3 , 6 . Hexagonal boron nitride (h-BN) is a dielectric two-dimensional material 7 with high strength (about 100 gigapascals) and elastic modulus (approximately 0.8 terapascals), which are similar to those of graphene 8 . Its fracture behaviour has long been assumed to be similarly brittle, subject to Griffith’s law 9 , 10 , 11 , 12 , 13 , 14 . Contrary to expectation, here we report high fracture toughness of single-crystal monolayer h-BN, with an effective energy release rate up to one order of magnitude higher than both its Griffith energy release rate and that reported for graphene. We observe stable crack propagation in monolayer h-BN, and obtain the corresponding crack resistance curve. Crack deflection and branching occur repeatedly owing to asymmetric edge elastic properties at the crack tip and edge swapping during crack propagation, which intrinsically toughens the material and enables stable crack propagation. Our in situ experimental observations, supported by theoretical analysis, suggest added practical benefits and potential new technological opportunities for monolayer h-BN, such as adding mechanical protection to two-dimensional devices.