Whereas frictionless exchange markets provide a high degree of liquidity for financial assets, investments in real assets and productive capacity may be very costly to modify, and thus effectively irreversible in the short-run. This paper addresses the problem of an investor (individual or enterprise) who must allocate a limited resource to productive investments over time. Investment opportunities arrive in a random sequence and are irreversible in the short-run: thus investment decisions are made under uncertainty as to future opportunities (which may have to be foregone). The analysis demonstrates that a rational investor will demand a higher return on long-lasting opportunities than on those which are instantaneously reversible. The liquidity premium increases with the average duration of the non-liquid investments.