The lack of superconductivity in several candidate materials that exhibit a non-spin density wave quantum critical point has raised the question of whether the associated spectra of quantum fluctuations are beneficial to forming superconducting electron pairs. Here we discuss the possibility that the prototypical heavy-fermion antiferromagnet CeRhIn5 may be the first example of unconventional superconductors where superconductivity arises from Kondo-breakdown quantum criticality.