We report the AGILE detection and the results of the multifrequency follow-up observations of a bright.-ray flare of the blazar 3C 279 in 2015 June. We use AGILE and Fermi gamma-ray data, together with Swift X-ray andoptical-ultraviolet data, and ground-based GASP-WEBT optical observations, including polarization information, to study the source variability and the overall spectral energy distribution during the.-ray flare. The.-ray flaring data, compared with as yet unpublished simultaneous optical data that will allow constraints on the big blue bump disk luminosity, show very high Compton dominance values of similar to 100, with the ratio of.-ray to optical emission rising by a factor of three in a few hours. The multiwavelength behavior of the source during the flare challenges one-zone leptonic theoretical models. The new observations during the 2015 June flare are also compared with already published data and nonsimultaneous historical 3C 279 archival data.