We propose a framework for studying the optimal design of rights relating to the control of an economic resource, which we broadly refer to as property rights. An agent makes an investment decision affecting her valuation for the resource, and then participates in a trading mechanism chosen by a principal in a sequentially rational way, leading to a hold-up problem. A designer—who would like to incentivize efficient investment and whose preferences may differ from those of the principal—can endow the agent with a menu of rights that determine the agent's outside options in the interaction with the principal. We characterize the optimal menu of rights as a function of the designer's and the principal's objectives, and the investment technology. The optimal menu requires at most two types of rights, including an option-to-own that grants the agent control over the resource upon paying a pre-specified price.