  The Wigner-crystal phase of two-dimensional electrons interacting via the
Coulomb repulsion and subject to a strong Rashba spin-orbit coupling is
investigated. For low enough electronic densities the spin-orbit band splitting
can be larger than the zero-point energy of the lattice vibrations. Then the
degeneracy of the lower subband results in a spontaneous symmetry breaking of
the vibrational ground state. The $60^{\circ}-$rotational symmetry of the
triangular (spin-orbit coupling free) structure is lost, and the unit cell of
the new lattice contains two electrons. Breaking the rotational symmetry also
leads to a (slight) squeezing of the underlying triangular lattice.
