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Growing observational evidence indicates that nebular line emission has a significant impact on the rest-frame optical fluxes of z∼ 5–7 galaxies. This line emission makes z∼ 5–7 galaxies appear more massive, with lower specific star-formation rates (sSFRs). However, corrections for this line emission have been difficult to perform reliably because of huge uncertainties on the strength of such emission at z≳ 5.5. In this paper, we present the most direct observational evidence thus far for ubiquitous high-equivalent-width (EW)[O iii]+ Hβ line emission in Lyman-break galaxies at z∼ 7, and we present a strategy for an improved measurement of the sSFR at z∼ 7. We accomplish this through the selection of bright galaxies in the narrow redshift window z∼ 6.6–7.0 where the Spitzer/Infrared Array Camera (IRAC) 4.5 μm flux provides a clean measurement of the stellar continuum light, in contrast with the 3.6 μm flux …