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 \pm 15 ) \times 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 \pm 11 ) \times 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 .