  In this paper, we prove pathwise uniqueness for stochastic degenerate systems
with a H{\"o}lder drift, for a H{\"o}lder exponent larger than the critical
value 2/3. This work extends to the degenerate setting the earlier results
obtained by Zvonkin, Veretennikov, Krylov and R{\"o}ckner from non-degenerate
to degenerate cases. The existence of a threshold for the H{\"o}lder exponent
in the degenerate case may be understood as the price to pay to balance the
degeneracy of the noise. Our proof relies on regularization properties of the
associated PDE, which is degenerate in the current framework and is based on a
parametrix method.
