We report the observation of nuclear resonant diffraction of synchrotron radiation by a synthetic multilayer. The nuclear period of the ${[}^{57}$Fe(22 \AA{})/Sc(11 \AA{})/Fe(22 \AA{})/Sc(11 \AA{})\ifmmode\times\else\texttimes\fi{}25 multilayer was chosen to be twice the electronic period to obtain a pure nuclear Bragg reflection. Strong enhancement of the radiative scattering channel provided a fast time response for the $^{57}\mathrm{Fe}$ resonant scattering at the Bragg peak, with a decay time of 4 ns. The nuclear multilayer will be useful as a narrow bandpass monochromator for synchrotron radiation.