While most of the intergalactic medium (IGM) today is permeated by ionized hydrogen, it was largely filled with neutral hydrogen for the first 700 million years after the big bang. The process that ionized the IGM (cosmic reionization) is expected to be spatially inhomogeneous, with fainter galaxies likely playing a significant role. However, we still have only a few direct constraints on the reionization process. Here we report spectroscopic confirmation of two galaxies and very likely a third galaxy in a group (hereafter EGS77) at redshift z = 7.7, merely 680 Myr after the big bang. The physical separation among the three members is <0.7 Mpc. We estimate the radius of ionized bubble of the brightest galaxy to be about 1.02 Mpc, and show that the individual ionized bubbles formed by all three galaxies likely overlap significantly, forming a large yet localized ionized region, indicative of inhomogeneity in the reionization process. It is striking that two of three galaxies in EGS77 are quite faint in the continuum, thanks to our selection using their Ly line emission in the narrowband filter. Indeed, one is the faintest spectroscopically confirmed galaxy yet discovered at such high redshifts. Our observations provide direct constraints on the process of cosmic reionization, and allow us to investigate the properties of sources responsible for reionizing the universe.