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In this paper we study the properties of the six optically dark galaxiesdetected in the 69 arcmin^2 GOODS-ALMA 1.1mm continuum survey. While none ofthem are listed in the deepest H-band based CANDELS catalog in the GOODS-Southfield down to H=28.16AB, we were able to de-blend two of them from their brightneighbor and measure an $H$-band flux for them. We note that AGS4 and AGS15have H=25.23, 27.11AB respectively. Their extreme proximity (0.50", 0.27") to abright optical source and their extreme faintness prevented them from beingincluded in the H-band catalog. We present the spectroscopic scan follow-up offive of the six sources with ALMA band 4. All are detected in the 2mm continuumwith signal-to-noise ratios higher than eight. One emission line is detected inAGS4 (\nu_{obs} =151.44GHz with a S/N=8.58) and AGS17 (\nu_{obs} =154.78GHzwith a S/N=10.23), which we interpret in both cases as being due to the CO(6-5)line at z^{AGS4}_{spec}=3.556 and z^{AGS4}_{spec}=3.467, respectively. Theseredshifts match both the probability distribution of the photometric redshiftsderived from the UV to near-infrared spectral energy distributions (SEDs) andthe far-infrared SEDs for typical dust temperatures of galaxies at theseredshifts. We present evidence that nearly 70% (4/6 of galaxies) of theoptically dark galaxies belong to the same overdensity of galaxies at z~3.5.overdensity The most massive one, AGS24 (M_{\star} = 10^{11.32^{+0.02}_{-0.19}}M_{\odot}), is the most massive galaxy without an active galactic nucleus (AGN)at $z$\,>\,3 in the GOODS-ALMA field. It falls in the very center of the peakof the galaxy surface density, which suggests that the surrounding overdensityis a proto-cluster in the process of virialization and that AGS24 is thecandidate progenitor of the future brightest cluster galaxy (BCG).

GOODS-ALMA: Optically dark ALMA galaxies shed light on a cluster in formation at z = 3.5