The AllDifferent constraint is a fundamental tool in Constraint Programming. It naturally arises in many problems, from puzzles to scheduling and routing applications. Such popularity has prompted an extensive literature on filtering and propagation for this constraint. Motivated by the benefits that GPUs offer to other branches of AI, this paper investigates the use of GPUs to accelerate filtering and propagation. In particular, we present an efficient parallelization of the AllDifferent constraint on GPU; we analyze different design and implementation choices and evaluates the performance of the resulting system on medium to large instances of the Travelling Salesman Problem with encouraging results.