We study the important problem of how a supplier should optimally share the consequences of demand uncertainty (i.e., the cost of inventory excesses and shortages) with a retailer in a two-level supply chain facing a finite planning horizon. In particular, we characterize a multi-period contract form, the promised lead time contract, that reduces the supplier's risk from demand uncertainty and the retailer's risk from uncertain inventory availability. Under the contract terms, the supplier guarantees on-time delivery of complete orders of any size after the promised lead time. We characterize the optimal promised lead time and the corresponding payments that the supplier should offer to minimize her expected inventory cost while ensuring the retailer's participation. In such a supply chain, the retailer often holds private information about his shortage cost (or his service level to end customers). Hence, to understand the impact of the promised lead time contract on th...