  Growing observational evidence now indicates that nebular line emission has a
significant impact on the rest-frame optical fluxes of z~5-7 galaxies observed
with Spitzer. This line emission makes z~5-7 galaxies appear more massive, with
lower specific star formation rates. However, corrections for this line
emission have been very difficult to perform reliably due to huge uncertainties
on the overall strength of such emission at z>~5.5. Here, we present the most
direct observational evidence yet for ubiquitous high-EW [OIII]+Hbeta line
emission in Lyman-break galaxies at z~7, while also presenting 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
IRAC 4.5 micron flux provides a clean measurement of the stellar continuum
light. Observed 4.5 micron fluxes in this window contrast with the 3.6 micron
fluxes which are contaminated by the prominent [OIII]+Hbeta lines. To ensure a
high S/N for our IRAC flux measurements, we consider only the brightest
(H_{160}<26 mag) magnified galaxies we have identified in CLASH and other
programs targeting galaxy clusters. Remarkably, the mean rest-frame optical
color for our bright seven-source sample is very blue, [3.6]-[4.5]=-0.9+/-0.3.
Such blue colors cannot be explained by the stellar continuum light and require
that the rest-frame EW of [OIII]+Hbeta be greater than 637 Angstroms for the
average source. The bluest four sources from our seven-source sample require an
even more extreme EW of 1582 Angstroms. Our derived lower limit for the mean
[OIII]+Hbeta EW could underestimate the true EW by ~2x based on a simple
modeling of the redshift distribution of our sources. We can also set a robust
lower limit of >~4 Gyr^-1 on the specific star formation rates based on the
mean SED for our seven-source sample. (abridged)
