1,3,5,7-Tetranitro-1,3,5,7-tetraazacyclooctane (HMX) is a major component of many explosives and propellants. Chemical kinetic simulations of the reactions of HMX require knowledge of its enthalpy, entropy, and heat capacity in the gas-phase and condensed phases. While some experimental measurements are available, most available thermochemical information has been obtained by analogy with the smaller species, RDX, and its reaction products. Using the Hartree-Fock method with the 6-31G* basis set we have calculated structures, vibrational frequencies, and bond strengths for the isolated HMX molecule and its two major reaction products. This, with some available experimental data, allows us to calculate the relevant thermochemical parameters for these species. With this information and some published experimental measurements of sublimation pressure, phase change enthalpies, and heat capacities, we have also calculated some thermochemical data for three condensed phases of HMX: beta-HMX, delta-HMX and liquid HMX. We present the thermochemical parameters in both the JANAF and CHEMKIN format. We also compare the current calculations with previous estimates.