Under homeotropic anchoring conditions, the first order nematic-choles
teric phase transition gives rise to localized spatial patterns called
cholesteric fingers. In this Letter we describe a new equilibrium str
ucture which, to our knowledge, has never been reported either numeric
ally or analytically, and we investigate its dynamics. This chiral pat
tern, which has broken the parity symmetry, is found to move when subm
itted to an ac electric voltage or to a white noise. Our result may ex
plain, at least qualitatively, the recent observations of spontaneous
spiral wave formations in cholesteric liquid crystal under the applica
tion of an ac electric voltage.