We report the detection by the AGILE (Astro-rivelatore Gamma a Immagini LEggero) satellite of an intense gamma-ray flare from the source AGL J1511-0909, associated with the powerful quasar PKS 1510-089, during ten days of observations from 23 August to 1 September 2007. During the observation period, the source was in optical decrease following a flaring event monitored by the GLAST-AGILE Support Program (GASP) of the Whole Earth Blazar Telescope (WEBT). The simultaneous gamma-ray, optical, and radio coverage allows us to study the spectral energy distribution and the theoretical models based on the synchrotron and inverse Compton (IC) emission mechanisms. AGILE observed the source with its two co-aligned imagers, the Gamma-Ray Imaging Detector and the hard X-ray imager Super-AGILE sensitive in the 30 MeV - 50 GeV and 18 - 60 keV bands, respectively. Between 23 and 27 August 2007, AGILE detected gamma-ray emission from PKS 1510-089 when this source was located about 50 degrees off-axis, with an average flux of (270 +/- 65) x 10^{-8} photons cm^{-2} s^{-1} for photon energy above 100 MeV. In the following period, 28 August - 1 September, after a satellite re-pointing, AGILE detected the source at about 35 degrees off-axis, with an average flux (E > 100 MeV) of (195 +/- 30) x 10^{-8} photons cm^{-2} s^{-1}. No emission was detected by Super-AGILE, with a 3-sigma upper limit of 45 mCrab in 200 ksec. The spectral energy distribution is modelled with a homogeneous one-zone synchrotron self Compton (SSC) emission plus contributions by external photons: the SSC emission contributes primarily to the X-ray band, whereas the contribution of the IC from the external disc and the broad line region match the hard gamma-ray spectrum observed. ; Comment: 5 pages, 5 figures, accepted for publication in A&A