Using first-principles methods, the phase stability of the underlying body-centered-cubic (bcc) structure of Ti3Al2V and slightly rearranged atomic structures are investigated. The calculated ground-state energies show an instability in the ternary Ti3Al 2V alloy with respect to the ω structure-type atomic displacement. A Mulliken population analysis shows strong bonding between the transition metals and Al. It is shown that Ti-Al is the strongest bond and that ω-type displacements increase the population overlap for this bond and reduce the energy of the system. The first-principles calculations are extended to finite temperature and various contributions to the free energy are calculated within the quasiharmonic approximation. It is shown that, at high temperatures, the bcc structure is stabilized by the contribution of the low-energy modes to lattice entropy. In agreement with experiment and in contrast to the Ti-Al-Nb system, we find that the metastable B82 structure cannot form in this alloy.