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 The $gamma$-ray flaring data, compared with as yet unpublished simultaneous optical data which allow to set constraints on the big blue bump disk luminosity, show very high Compton dominance values of $sim 100$, with a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