  I present first principles calculations of the phonon dispersions of TiSe$_2$
in the $P\overline{3}c1$ phase, which is the currently accepted low-temperature
structure of this material. They show weak instabilities in the acoustic
branches in the out-of-plane direction, suggesting that this phase may not be
the true ground state. To find the lowest energy structure, I study the
energetics of all possible distorted structures corresponding to the isotropy
subgroups of $P\overline{3}m1$ for the $M_1^-$ and $L_1^-$ phonon instabilities
present in this high-temperature phase at $q = (\frac{1}{2},0,0)$ and
$(\frac{1}{2},0,\frac{1}{2})$, respectively. I was able to stabilize 10
different structures that are lower in energy relative to the parent
$P\overline{3}m1$ phase, including two monoclinic structures more energetically
stable than the $P\overline{3}c1$ phase. The lowest energy structure has the
space group $C2$ with the order parameter $M_1^- (a,0,0) + L_1^- (0,b,b)$. This
structure lacks inversion symmetry, and its primitive unit cell has 12 atoms.
