Context : Neuhäuser & Comerón ( 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 H \alpha 2 , classified as brown dwarf candidate in several publications and suggested as possible binary in Neuhäuser et al . ( 2002 ) . Aims : We have searched around Cha H \alpha 2 for close and faint companions with adaptive optics imaging . Methods : 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 together with a Hipparcos binary for astrometric calibration . Moreover , we took a J-band image in March 2007 to get color information . 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 . Results : We find Cha H \alpha 2 to be a very close binary of \sim 0.16 arcsec separation , having a flux ratio of \sim 0.91 , thus having almost equal brightness and indistinguishable spectral types within the errors . We show that the two tentative components of Cha H \alpha 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 \pm 100 K , corresponding to a spectral type of M6 \pm 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 } \simeq 4.3 mag from this comparison . Conclusions : We derive masses of \sim 0.110 M _ { \odot } ( \geq 0.070 M _ { \odot } ) and \sim 0.124 M _ { \odot } ( \geq 0.077 M _ { \odot } ) for the two components of Cha H \alpha 2 , i.e. , probably low-mass stars , but one component could possibly be a brown dwarf .