Pristine graphene is the strongest material ever measured. However, large-area graphene films produced by means of chemical vapor deposition (CVD) are polycrystalline and thus contain grain boundaries that can potentially weaken the material. We combined structural characterization by means of transmission electron microscopy with nanoindentation in order to study the mechanical properties of CVD-graphene films with different grain sizes. We show that the elastic stiffness of CVD-graphene is identical to that of pristine graphene if postprocessing steps avoid damage or rippling. Its strength is only slightly reduced despite the existence of grain boundaries. Indentation tests directly on grain boundaries confirm that they are almost as strong as pristine. Graphene films consisting entirely of well-stitched grain boundaries can retain ultrahigh strength, which is critical for a large variety of applications, such as flexible electronics and strengthening components.