  We investigate broken rotational symmetry (BRS) states for the fractional
quantum Hall effect (FQHE) at 1/3-filling of the valence Landau level (LL).
Recent Monte Carlo calculations by Musaelian and Joynt [J. Phys.: Condens.\
Matter {\bf 8}, L105 (1996)] suggest that Laughlin's state becomes unstable to
a BRS state for some critical finite thickness value. We study in detail the
properties of such state by performing a hypernetted-chain calculation that
gives results in the thermodynamic limit, complementing other methods which are
limited to a finite number of particles. Our results indicate that while
Laughlin's state is stable in the lowest LL, in higher LLs a BRS instability
occurs, perhaps indicating the absence of FQHE at partial fillings of higher
LLs. Possible connections to the newly discovered liquid crystalline phases in
higher LLs are also discussed.
