Make and document every attempt to persuade the problem person to comply with project requirements.
If replacing the problem person doesn't represent a significant difficulty, do that.
Try to find out why the problem person isn't performing and, if possible, remove the barrier (coach, provide different resources, arrange for training, etc.)
Discuss the situation with the problem person's immediate supervisor, clearly detailing your documentation and ask for his/her guidance in resolving the issue.
Only after exhausting the steps above, ask someone with sufficient authority to demand compliance. Have this person (probably the supervisor you've talked with) set a clear expectation that if compliance is not forthcoming, a Performance Improvement Plan will be.
If the performance shortfall is not skill based and poses an immediate threat to the project deadline, try to move through the steps above as quickly as possible. That said, remember that, even under the tightest deadlines, a premature exercise of raw authority will send a very chilling effect through your project team.