We design an incentive-compatible mechanism for schedulingn non-malleable parallel jobs on a parallel system comprising m identical processors. Each job is owned by a selfish user who is rational: she performs actions that maximize her welfare even though doing so may cause system-wide suboptimal performance. Each job is characterized by four parameters: value, deadline, number of processors, and execution time. The user's welfare increases by the amount indicated by the value if her job can be completed by the deadline. The user declares theparameters to the mechanism which uses them to compute the schedule and the payments. The user can misreport the parameters, but since the mechanism is incentive-compatible, she chooses to truthfully declare them. We prove the properties of the mechanism and perform a study by simulation.