Neuhaeuser & Comeron (1998, 1999) 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 Halpha 2, classified as brown dwarf candidate in several publications and suggested as possible binary in Neuhaeuser et al. (2002). We have searched around Cha Halpha 2 for close and faint companions with adaptive optics imaging. Two epochs of direct imaging data were taken with the Very Large Telescope (VLT) Adaptive Optics instrument NACO in February 2006 and March 2007 in Ks-band. We retrieved an earlier image from 2005 from the European Southern Observatory (ESO) Science Archive Facility, increasing the available time coverage. After confirmation of common proper motion, we deduce physical parameters of the objects by spectroscopy, like temperature and mass. We find Cha Halpha 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 Halpha 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. We derive masses of ~0.110 Msun (>0.070 Msun) and ~0.124 Msun (>0.077 Msun) for the two components of Cha Halpha 2, i.e., probably low-mass stars, but one component could possibly be a brown dwarf.