Successful attempts to manufacture synthetic molecular motors have recently been reported(1,2). However, compared with natural systems such as motor proteins(3-6), synthetic motors are smaller molecules and are therefore subject to thermal fluctuations that prevent them from performing any useful function(7). A mechanism is needed to amplify the single molecular motion to such a level that it becomes distinguishable from the thermal background. Condensation of molecular motors into soft ordered phases ( such as liquid crystals) will be a feasible approach, because there is evidence that they support molecularly driven non-equilibrium motions(8-10). Here we show that a chiral liquid-crystalline monolayer spread on a glycerol surface acts as a condensed layer of molecular rotors, which undergo a coherent molecular precession driven by the transmembrane transfer of water molecules. Composed of simple rod-like molecules with chiral propellers, the monolayer exhibits a spatiotemporal pattern in molecular orientations that closely resembles 'target patterns' in Belousov-Zhabotinsky reactions(11). Inversion of either the molecular chirality or the transfer direction of water molecules reverses the rotation direction associated with switching from expanding to converging target patterns. Endowed only with the soft directional order, the liquid crystal is an optimal medium that helps molecular motors to manifest their individual motions collectively.