We show that a monodomain chiral smectic C elastomer exhibits a biaxial shape memory effect, demonstrating its spontaneous and reversible deformation in a heating and cooling process where successive phase transitions take place. Not only shrinkage (elongation) due to the smectic-isotropic (isotropic-smectic) transition but also spontaneous shear-deformation associated with molecular tilting in the smectic phases is observed. In addition, we discuss the relationship between the deformation of the monodomain elastomer and the local symmetry of liquid-crystalline phases by means of X-ray scattering observation.