We use the ultra-deep WFC3/IR data over the Hubble Ultra Deep Field 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 β in these galaxies, and compare the slopes with galaxies at later times to measure the evolution in β. For luminous L*z=3 galaxies, we measure a mean UV-continuum slope β of −2.0 ± 0.2, which is comparable to the β ∼ −2 derived at similar luminosities at z ∼ 5–6. However, for the lower luminosity 0.1L*z=3 galaxies, we measure a mean β 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 β of −3.0 can be matched by a very young, dust-free stellar population, but when nebular emission is included the expected β becomes ⩾−2.7. To produce these very blue βs (i.e., β ∼ −3), extremely low metallicities and mechanisms to reduce the red nebular emission seem to be required. For example, a large escape fraction (i.e., fesc ≳ 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.