  We consider multidimensional conservation laws perturbed by multiplicative
L\'{e}vy noise. We establish existence and uniqueness results for entropy
solutions. The entropy inequalities are formally obtained by the
It\^{o}-L\'{e}vy chain rule. The multidimensionality requires a generalized
interpretation of the entropy inequalities to accommodate Young measure-valued
solutions. We first establish the existence of entropy solutions in the
generalized sense via the vanishing viscosity method, and then establish the
$L^1$-contraction principle. Finally, the $L^1$ contraction principle is used
to argue that the generalized entropy solution is indeed the classical entropy
solution.
