  We prove uniqueness in law for possibly degenerate SDEs having a linear part
in the drift term. Diffusion coefficients corresponding to non-degenerate
directions of the noise are assumed to be continuous. When the diffusion part
is constant we recover the classical degenerate Ornstein-Uhlenbeck process
which only has to satisfy the H\"ormander hypoellipticity condition. In the
proof we use global $L^p$-estimates for hypoelliptic Ornstein-Uhlenbeck
operators recently proved in Bramanti-Cupini-Lanconelli-Priola (Math. Z. 266
(2010)) and adapt the localization procedure introduced by Stroock and
Varadhan. Appendix contains a quite general localization principle for
martingale problems.
