The bulk modulus of a natural sample of cubic majorite, one of the primary components of the Earth's transition zone, has been determined by two independent methods: quasi-hydrostatic compression in the diamond anvil cell and Brillouin spectroscopy at room pressure. The two measurements agree well, and together yield a zero-pressure isothermal bulk modulus KOT=162.7(¿3.3) GPa, and a pressure derivative KOT'=6.6(¿0.8). Additional compression experiments under nonhydrostatic conditions show that majorite supports shear stresses of at least 2 to 3 GPa at pressures of 7--11 GPa, among the highest values yet documented in silicates or oxides at comparable pressures. These results imply a high strength for majorite, suggesting that the transition zone could be strong to a degree that may influence deformation and heat transfer within the Earth. ¿ 2000 American Geophysical Union