  It is demonstrated that under common conditions a molecular solid subject to
Jahn-Teller interactions supports stable Q-ball-like non-topological solitons.
Such solitons represent a localized lump of excess electric charge in periodic
motion accompanied by a time-dependent shape distortion of a set of adjacent
molecules. The motion of the distortion can correspond to a true rotation or to
a pseudo-rotation about the symmetric shape configuration. These solitons are
stable for Jahn-Teller coupling strengths below a critical value; however, as
the Jahn-Teller coupling approaches this critical value, the size of the
soliton diverges signaling an incipient structural phase transition. The
soliton phase mimics features commonly attributed to phase separation in
complex solids.
