Nearly all existing methods for stereo reconstruction assume that scene reflectance is Lambertian, and make use of color constancy as a matching invariant. We introduce a new invariant for stereo reconstruction called Light Transport Constancy, which allows completely arbitrary scene reflectance (BRDFs). This invariant can be used to formulate a rank constraint on multiview stereo matching when the scene is observed in several lighting configurations. In addition, we show that this multiview constraint can be used with as few as two cameras and two lighting configurations. Unlikely previous methods for BRDF invariant stereo, Light Transport Constancy does not require precisely configured or calibrated light sources, nor calibration objects in the scene. Importantly, the new constraint can be used to provide BRDF invariance to any existing stereo method, whenever appropriate lighting variation is available.