Thanks to its outstanding angular resolution, the Atacama Large Millimeter/submillimeter Array (ALMA) has recently unambiguously identified a population of optically dark galaxies with redshifts greater than z = 3, which play an important role in the cosmic star formation in massive galaxies. In this paper we study the properties of the six optically dark galaxies detected in the 69 arcmin² GOODS-ALMA 1.1 mm continuum survey. While none of them are listed in the deepest H-band based CANDELS catalog in the GOODS-South field down to H = 28.16 AB, we were able to de-blend two of them from their bright neighbor and measure an H-band flux for them. We present the spectroscopic scan follow-up of five of the six sources with ALMA band 4. All are detected in the 2 mm continuum with signal-to-noise ratios higher than eight. One emission line is detected in AGS4 (ν_obs = 151.44 GHz with an S/N = 8.58) and AGS17 (ν_obs = 154.78 GHz with an S/N = 10.23), which we interpret in both cases as being due to the CO(6–5) line at z_spec^AGS4 = 3.556 and z_spec^AGS17 = 3.467, respectively. These redshifts match both the probability distribution of the photometric redshifts derived from the UV to near-infrared spectral energy distributions (SEDs) and the far-infrared SEDs for typical dust temperatures of galaxies at these redshifts. We present evidence that nearly 70% (4/6 of galaxies) of the optically dark galaxies belong to the same overdensity of galaxies at z ∼ 3.5. overdensity The most massive one, AGS24 (M_⋆ = 10^{11.32_−0.19+0.02} M_⊙), is the most massive galaxy without an active galactic nucleus at z > 3 in the GOODS-ALMA field. It falls in the very center of the peak of the galaxy surface density, which suggests that the surrounding overdensity is a proto-cluster in the process of virialization and that AGS24 is the candidate progenitor of the future brightest cluster galaxy.