We have observed Bragg diffraction of a Bose-Einstein condensate of sodium
atoms by a moving, periodic, optical potential. The coherent process of Bra
gg diffraction produced a splitting of the condensate with unidirectional m
omentum transfer. Using the momentum selectivity of the Bragg process, we s
eparated a condensate component with a momentum width narrower than that of
the original condensate. By repeatedly pulsing the optical potential while
the atoms were trapped, we observed the trajectory of the split atomic wav
e packets in the confining magnetic potential.