We report fracture toughness measurements on single crystals of YBa2Cu3Ox, the phase responsible for superconductivity above liquid‐nitrogen temperatures. Indentation crack length measurements on the (010) orthorhombic crystal growth faces revealed the (100) and (001) planes as preferred fracture planes. The toughness of these planes isKc=1.1±0.3 MPa m1/2, and the hardnessH=8.7±2.4 GPa. The observed growth of both radial and lateral cracks in ambient air suggests that these crystals are susceptible to moisture‐enhanced nonequilibrium crack propagation.