We report on a method for tomographic phase contrast imaging of centimeter sized objects. As opposed to existing techniques, our approach can be used with low-brilliance, lab based X-ray sources and thus is of interest to a wide range of applications in medicine, biology, and non-destructive testing. The work is based on the recent development of a hard X-ray grating interferometer, which has been demonstrated to yield differential phase contrast projection images. Here we particularly focus on how this method can be used for tomographic reconstructions using filtered backprojection algorithms to yield quantitative volumetric information of the real part of the samples's refractive index.