In situ neutron diffraction experiments show that at pressures above 2 kilobars, cubic zirconium tungstate (ZrW2O8) undergoes a quenchable phase transition to an orthorhombic phase, the structure of which has been solved from powder diffraction data. This phase transition can be reversed by heating at 393 kelvin and 1 atmosphere and involves the migration of oxygen atoms in the lattice. The high-pressure phase shows negative thermal expansion from 20 to 300 kelvin. The relative thermal expansion and compressibilities of the cubic and orthorhombic forms can be explained in terms of the "cross-bracing" between polyhedra that occurs as a result of the phase transition.