  We report on the first observation of Bragg scattering of an ultracold $^6$Li
Fermi gas. We demonstrate a Ramsey-type matter-wave interferometer based on
Bragg diffraction and find robust signatures of persistent matter wave
coherences using an echo pulse sequence. Because of the Pauli principle, the
diffracted fermions oscillate nearly unperturbed in the trapping potential for
long times beyond 2 s. This suggests extremely long coherence times. On these
timescales, only the presence of a $^{87}$Rb cloud seems sufficient to induce
noticeable perturbations.
