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 ∼2.67 northwest of CT Cha corresponding to a projected separation of ∼440 AU at 165 ± 30 pc. We show that CT Cha A and this faint object form a common proper motion pair and that the companion is by ≥4σ significance not a stationary background object. The near-infrared spectroscopy yields a temperature of 2600 ± 250 K for the companion and an optical extinction of A V = 5.2 ± 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 ≤0.01. Due to a prominent Pa-β emission in the J-band, accretion is probably still ongoing onto the CT Cha companion. From temperature and luminosity (log(L bol /L ) = -2.68 ± 0.21), we derive a radius of R = 2.20 +0.81 −0.60 R Jup . We find a consistent mass of M = 17 ± 6 M 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.