We consider a project supply chain where a manufacturer carries out a sequence of tasks, and each task requires certain key materials from a supplier. Since a fixed-price contract cannot attain channel coordination, we focus on time-based incentive contracts. Our proposed contract requires optimization of the material delivery schedule as well as the fraction and the timing of a delayed payment to each supplier. Under the contract, the manufacturer’s profit is affected by the variance but not by the mean of a supplier’s lead time. Each supplier benefits from a reduction in the mean or variance of his own lead time, whereas the supplier’s profit is independent of the duration of the on-site tasks and the lead times of other suppliers. The contract is also robust in various scenarios: in particular, coordination can be achieved even if the manufacturer’s estimate of the average delivery lead time is inaccurate.