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tokens: We thank Kristian Finlator, Brian Siana, Rychard Bouwens, Pascal Oesch, Dan Jaffe, and Jon Trump for useful conversations. S.L.F. acknowledges support from the University of Texas at Austin College of Natural Sciences. M.S. was supported by a NASA Astrophysics and Data Analysis Program award issued by JPL/Caltech. R.J.M. acknowledges ERC funding via the award of a consolidator grant. This work is based on observations made with the NASA/ESA Hubble Space Telescope , obtained at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555. These observations are associated with program #12060. This work is also based in part on observations made with the Spitzer Space Telescope , which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under a contract with NASA. Support for this work was provided by NASA through an award issued by JPL/Caltech.