Context. Neuhäuser & Comerón (1998, Science, 282, 83; 1999, A&A, 350, 612) presented direct imaging evidence, as well as first spectra, of several young stellar and sub-stellar M6-to M8-type objects in the Cha I dark cloud. One of these objects is Cha Hα 2, classified as brown dwarf candidate in several publications and suggested as possible binary in Neuhäuser et al. (2002, A&A, 384, 999 After confirmation of common proper motion, we deduce physical parameters of the objects by spectroscopy, like temperature and mass. Results. We find Cha Hα 2 to be a very close binary of ∼0.16 arcsec separation, having a flux ratio of ∼0.91, thus having almost equal brightness and indistinguishable spectral types within the errors. We show that the two tentative components of Cha Hα 2 form a common proper motion pair, and that neither component is a non-moving background object. We even find evidence for orbital motion. A combined spectrum of both stars spanning optical and near-infrared parts of the spectral energy distribution yields a temperature of 3000 ± 100 K, corresponding to a spectral type of M6 ± 1 and a surface gravity of log g = 4.0 +0.75 −0.5 , both from a comparison with GAIA model atmospheres. Furthermore, we obtained an optical extinction of A V 4.3 mag from this comparison. Conclusions. We derive masses of ∼0.110 M (≥0.070 M ) and ∼0.124 M (≥0.077 M ) for the two components of Cha Hα 2, i.e., probably low-mass stars, but one component could possibly be a brown dwarf.