In a recent experiment, Freedman and Clauser have found that Bell's inequality for local hidden-variable theories is violated by over six standard deviations. We derive an inequality similar to Bell's for nonlocal hidden-variable theories in which the hidden-variable density distribution of the particles measured is nonlocal, but where the detectors are contained within some finite volume. The measurement of Freedman and Clauser is used to put a lower limit on the nonlocality of the hidden-variable density distributions of the photons detected in their experiment. 1973 The American Physical Society.