Aims. Since the CGRO operation in 1991–2000, one of the primary unresolved questions about the blazar γ-ray emission has been its possible correlation with the low-energy (in particular optical) emission. To help answer this problem, the Whole Earth Blazar Telescope (WEBT) consortium has organized the GLAST-AGILE Support Program (GASP) to provide the optical-to-radio monitoring data to be compared with the γ-ray detections by the AGILE and GLAST satellites. This new WEBT project started in early September 2007, just before a strong γ-ray detection of 0716+714 by AGILE. Methods. We present the GASP-WEBT optical and radio light curves of this blazar obtained in July–November 2007, about various AGILE pointings at the source. We construct NIR-to-UV spectral energy distributions (SEDs), by assembling GASP-WEBT data together with UV data from the Swift ToO observations of late October. Results. We observe a contemporaneous optical-radio outburst, which is a rare and interesting phenomenon in blazars. The shape of the SEDs during the outburst appears peculiarly wavy because of an optical excess and a UV drop-and-rise. The optical light curve is well sampled during the AGILE pointings, showing prominent and sharp flares. A future cross-correlation analysis of the optical and AGILE data will shed light on the expected relationship between these flares and the γ-ray events.