We use the ultra-deep WFC3/IR data over the HUDF and the Early Release Science WFC3/IR data over the CDF-South GOODS field to quantify the broadband spectral properties of candidate star-forming galaxies at z~7. We determine the UV-continuum slope beta in these galaxies, and compare the slopes with galaxies at later times to measure the evolution in beta. For luminous L*(z=3) galaxies, we measure a mean UV-continuum slope beta of -2.0+/-0.2, which is comparable to the beta~-2 derived at similar luminosities at z~5-6. However, for the lower luminosity 0.1L*(z=3) galaxies, we measure a mean beta of -3.0+/-0.2. This is substantially bluer than is found for similar luminosity galaxies at z~4, just 800 Myr later, and even at z~5-6. In principle, the observed beta of -3.0 can be matched by a very young, dust-free stellar population, but when nebular emission is included the expected beta becomes >~-2.7. To produce these very blue betas (i.e., beta~-3), extremely low metallicities and mechanisms to reduce the red nebular emission are likely required. For example, a large escape fraction (i.e., f_{esc}>~0.3) could minimize the contribution from this red nebular emission. If this is correct and the escape fraction in faint z~7 galaxies is >~0.3, it may help to explain how galaxies reionize the universe.
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