Although the vast majority of real options models assume that investment opportunities are permanently available, many real-world investment opportunities are sporadic. Options to invest can suddenly become blacked-out, only to be followed by a re-opening in the future. For example, the option to develop real estate may open or close depending upon zoning and growth control decisions, competitive entry, or input (labor or material) availability. Similar factors influence complex R&D options. We term such randomly recurring investment opportunities as options on illiquid projects. We derive and analyze a model of such illiquid options, and find that the potential for exercise opportunities to be shut down provides an incentive for early exercise while the investment opportunity is open. We examine the conditions that impact the liquidity discount. We also consider the case in which the degree of illiquidity is endogenously determined, for instance by a regulator. The model is extended to an equilibrium setting, and the notion of illiquidity is generalized to allow for costly exercise during times of illiquidity.