A chiral liquid crystalline elastomer (CLCE) actuator is demonstrated. The solution-cast polydomain film of CLCE can twist upon order-disorder phase transition without any preset alignment of mesogens. The handedness of twisting is specific to the molecular chirality of the chiral dopant in the CLCE structure, while the degree of twisting, in terms of helical pitch and diameter, is sensitive to the aspect ratio and the thickness of the CLCE strip as well as the chiral dopant content. This phenomenon appears to stem from the local twisting forces and deformations of randomly oriented helical domains, which cannot cancel each other out due to the chirality and thus result in a macroscopic "chiral" force acting on the CLCE actuator. This finding reveals a materials design for preparing twisting LCE actuators.