We present the analysis of deep HST multi-band imaging of the BDF field specifically designed to identify faint companions around two of the few Ly-alpha emitting galaxies spectroscopically confirmed at z~7 (Vanzella et al. 2011). Although separated by only 4.4 proper Mpc these galaxies cannot generate HII regions large enough to explain visibility of their Ly-alpha line, thus requiring a population of fainter ionizing sources in their vicinity. We use deep HST and VLT-Hawk-I data to select z~7 Lyman break galaxies around the emitters. We select 6 new robust z~7 LBGs at Y~26.5-27.5 whose average spectral energy distribution is consistent with the objects being at the redshift of the close-by Ly-alpha emitters. The resulting number density of z~7 LBGs in the BDF field is a factor ~3-4 higher than expected in random pointings of the same size. We compare these findings with cosmological hydrodynamic plus radiative transfer simulations of a universe with a half neutral IGM: we find that indeed Ly-alpha emitter pairs are only found in completely ionized regions characterized by significant LBG overdensities. Our findings match the theoretical prediction that the first ionization fronts are generated within significant galaxy overdensities and support a scenario where faint, "normal" star-forming galaxies are responsible for reionization.