  We demonstrate that the two-dimensonal electron system in a strong
perpendicular magnetic field has stable states which break rotational but not
translational symmetry. The Laughlin fluid becomes unstable to these states in
quantum wells whose thickness exceeds a critical value which depends on the
electron density. The order parameter at 1/3 reduced density resembles that of
a nematic liquid crystal, in that a residual two-fold rotation axis is present
in the low symmetry phase. At filling factors 1/5 and 1/7, there are states
with four- and six-fold axes, as well. We discuss the experimental detection of
these phases.
