The coefficient of thermal expansion of ZrMgMo3O12 has been measured and was found to be extremely close to zero over a wide temperature range including room temperature ( = (1.6 ± 0.2) × 10–7 K–1 from 25 to 450 °C by X-ray diffraction (XRD)). ZrMgMo3O12 belongs to the family of AMgM3O12 materials, for which coefficients of thermal expansion have previously been reported to range from low-positive to low-negative. However, the low thermal expansion property had not previously been explained because atomic position information was not available for any members of this family of materials. We determined the structure of ZrMgMo3O12 by nuclear magnetic resonance (NMR) crystallography, using 91Zr, 25Mg, 95Mo, and 17O magic angle spinning (MAS) and 17O multiple quantum MAS (MQMAS) NMR in conjunction with XRD and density functional theory calculations. The resulting structure was of sufficient detail that the observed zero thermal expansion could be explained using quantitative measures of the properties of the coordination polyhedra. We also found that ZrMgMo3O12 shows significant ionic conductivity, a property that is also related to its structure. ; NSERC