In situ neutron powder diffraction measurements show that the orthorhombic-to-tetragonal phase transition in $\mathrm{Y}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-x}$, which occurs near 700°C in a pure oxygen atmosphere, is an order-disorder transition in which the disordering of oxygen atoms into a normally vacant site destroys the one-dimensional Cu-O chains present in the room-temperature orthorhombic structure. For both structures, the oxygen stoichiometry decreases monotonically with increasing temperature. The transition temperature depends on the oxygen partial pressure and occurs when the stoichiometry is near Y${\mathrm{Ba}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{6.5}$. The tetragonal structure has a partially occupied, nearly octahedral Cu-O arrangement, in contrast to the orthorhombic structure which has one-dimensional Cu-O chains. The observed depression of the superconducting transition temperature in tetragonal $\mathrm{Y}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-x}$, which has been quenched from high temperature, could result either from the disordering of oxygen atoms which destroys the one-dimensional chains or from the absence of ${\mathrm{Cu}}^{3+}$ ions.