  Let G be an unramified reductive group over a non archimedian local field F.
The so-called "Langlands Fundamental Lemma" is a family of conjectural
identities between orbital integrals for G(F) and orbital integrals for
endoscopic groups of G. In this paper we prove the Langlands fundamental lemma
in the particular case where F is a finite extension of F_p((t)), G is a
unitary group and p>rank(G). Waldspurger has shown that this particular case
implies the Langlands fundamental lemma for unitary groups of rank <p when F is
any finite extension of Q_p.
  We follow in part a strategy initiated by Goresky, Kottwitz and MacPherson.
Our main new tool is a deformation of orbital integrals which is constructed
with the help of the Hitchin fibration for unitary groups over projective
curves.
