  We report the gamma-ray activity from the Intermediate BL Lac S5 0716+714
during 2007 September-October observations by the AGILE satellite, coincident
with a period of intense optical activity of the source monitored by GASP-WEBT.
AGILE observed the source with its two co-aligned imagers, the Gamma-Ray
Imaging Detector (GRID) and the hard X-ray imager (Super-AGILE) sensitive in
the energy range 30 MeV-50 GeV and 18-60 keV respectively, in two different
periods: the first between 4 and 23 September 2007, the second between 24
October and 1 November 2007. Over the period 7-12 September, AGILE detected
gamma-ray emission from the source at a significance level of 9.6-sigma with an
average flux (E>100 MeV) of (97+/-15) x 10^{-8} photons cm^{-2} s^{-1},
increasing by a factor of at least four within three days. No emission was
detected by Super-AGILE in the energy range 18-60 keV, with a 3-sigma upper
limit of 10 mCrab in 335 ksec. The gamma-ray flux of S5 0716+714 detected by
AGILE is the highest ever detected for this blazar and one of the most intense
gamma-ray fluxes detected from a BL Lac object. The Spectral Energy
Distribution (SED) of mid-September seems to be consistent with the synchrotron
self-Compton (SSC) emission model, but only by including two SSC components
with different variability. In October 2007 AGILE repointed toward S5 0716+714
following an intense optical flare, measuring an average flux of (47+/-11) x
10^{-8} photons cm^{-2} s^{-1} at a significance level of 6.0-sigma. The
gamma-ray flux during both AGILE pointings appears to be highly variable on
timescales of 1 day.
