A new method for measuring spatial coherence in which optical fibers replace the traditional slits in Young's experiment is developed. The beam is sampled by the fiber ends, and the phase difference that causes the fringes is introduced by translating one fiber along its long axis by a few wavelengths. The technique has several advantages over the slit method: The fibers can be moved to arbitrarily chosen points, as opposed to removing and replacing sets of slits, giving greater flexibility in measurement as well as easing alignment problems. This method also does not rely on diffraction, and therefore enables measurement of much dimmer beams and dimmer points on beams. One can take as many data points as desired, thus tracing the shape of the coherence function accurately, whereas with slits one is restricted to the number of slit sets available. Finally, one does not have to assume beam symmetry. Although the magnitude of the spatial coherence function is not accurately reproduced, this can be corrected for, and the ability to reproduce the shape of the beam remains a useful measurement tool. We report, in particular, measurements of spatial coherence of a single-stripe diode laser, as well as a HeNe laser.