Context : Aims : In our ongoing search for close and faint companions around T Tauri stars in the Chamaeleon star-forming region , we here present observations of a new common proper motion companion to the young T-Tauri star and Chamaeleon member CT Cha and discuss its properties in comparison to other young , low-mass objects and to synthetic model spectra from different origins . Methods : Common proper motion of the companion and CT Cha was confirmed by direct Ks-band imaging data taken with the VLT Adaptive Optics ( AO ) instrument NACO in February 2006 and March 2007 , together with a Hipparcos binary for astrometric calibration . An additional J-band image was taken in March 2007 to obtain color information for a first classification of the companion . Moreover , AO integral field spectroscopy with SINFONI in J , and H+K bands was obtained to deduce physical parameters of the companion , such as temperature and extinction . Relative flux calibration of the bands was achieved using photometry from the NACO imaging data . Results : We found a very faint ( Ks = 14.9 mag , Ks _ { 0 } = 14.4 mag ) object , just \sim 2.67″ northwest of CT Cha corresponding to a projected separation of \sim 440 AU at 165 \pm 30 pc . We show that CT Cha A and this faint object form a common proper motion pair and that the companion is by \geq 4 \sigma significance not a stationary background object . The near-infrared spectroscopy yields a temperature of 2600 \pm 250 K for the companion and an optical extinction of A _ { V } = 5.2 \pm 0.8 mag , when compared to spectra calculated from Drift-Phoenix model atmospheres . We demonstrate the validity of the model fits by comparison to several other well-known young sub-stellar objects . Conclusions : We conclude that the CT Cha companion is a very low-mass member of Chamaeleon and very likely a physical companion to CT Cha , as the probability for a by chance alignment is \leq 0.01 . Due to a prominent Pa- \beta emission in the J-band , accretion is probably still ongoing onto the CT Cha companion . From temperature and luminosity ( \log ( L _ { bol } / L _ { \odot } ) = –2.68 \pm 0.21 ) , we derive a radius of R= 2.20 _ { -0.60 } ^ { +0.81 } R _ { \mathrm { Jup } } . We find a consistent mass of M= 17 \pm 6 M _ { \mathrm { Jup } } for the CT Cha companion from both its luminosity and temperature when placed on evolutionary tracks . Hence , the CT Cha companion is most likely a wide brown dwarf companion or possibly even a planetary mass object .