A rotational band with seven gamma-ray transitions between states with spin 2 Planck's constant and 16 Planck's constant has been observed in the doubly magic, self-conjugate nucleus (40)(20)Ca(20). The measured transition quadrupole moment of 1.80(+0.39)(-0.29)eb indicates a superdeformed shape with a deformation beta(2) = 0.59(+0.11)(-0.07). The features of this band are explained by cranked relativistic mean field calculations to arise from an 8-particle 8-hole excitation.