It is shown that the maximum velocity attainable by a laser-driven light sail is constrained by the back pressure of the relativistically transformed microwave background radiation field with interstellar material having little effect. Using current sail concepts, terminal Lorentz factors much in excess of 10 are not possible, and therefore, limitations are imposed on the benefits of relativistic time dilation and the possible use of such sails for travel over long interstellar distances. This is a fundamental constraint imposed by nature on the ultimate performance of such sails.