The title compound, thallium magnesium trichloride, has been identified as a scintillator with both moderate gamma-stopping power and moderate light yield. Knowledge of its crystal structure is needed for further development. This work determines the crystal structure of TlMgCl3 to be hexa-gonal P63/mmc (No. 194) and isostructural with RbMgCl3, contrary to previously reported data. This structure was obtained by single-crystal X-ray diffraction and was further confirmed by neutron diffraction measurements. Extending neutron diffraction measurements to high temperature, the data show that TlMgCl3 maintains this crystal structure from 290 K up through 725 K, approaching the melting point of 770 K. Anisotropic thermal expansion coefficients increase over this temperature range, from 31 to 38 × 10-6 K-1 along the a axis and from 19 to 34 × 10-6 K-1 along the c axis.