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 \sim 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 \pm 0.2 , which is comparable to the \beta \sim - 2 derived at similar luminosities at z \sim 5 - 6 . However , for the lower luminosity 0.1 L _ { z = 3 } ^ { * } galaxies , we measure a mean \beta of -3.0 \pm 0.2 . This is substantially bluer than is found for similar luminosity galaxies at z \sim 4 , just 800 Myr later , and even at z \sim 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 \geq - 2.7 . To produce these very blue \beta ’ s ( i.e. , \beta \sim - 3 ) , extremely low metallicities and mechanisms to reduce the red nebular emission seem to be required . For example , a large escape fraction ( i.e. , f _ { esc } \gtrsim 0.3 ) could minimize the contribution from this red nebular emission . If this is correct and the escape fraction in faint z \sim 7 galaxies is \gtrsim 0.3 , it may help to explain how galaxies reionize the universe .