In our ongoing search for close and faint companions around T Tauri stars, we found a very faint (Ks=14.9mag, Ks_0=14.4mag) object, just ~2.67 northwest of the Chamaeleon star-forming region member CT Cha corresponding to a projected separation of ~440AU at 165+/-30 pc. We show that CT Cha A and this faint object form a common proper motion pair from data of the VLT Adaptive Optics (AO) instrument NACO taken in February 2006 and March 2007 and that the companion is by >=4 sigma significance not a stationary background object. Our AO integral field spectroscopy with SINFONI in J, and H+K bands yields a temperature of 2600+/-250K for the companion and an optical extinction of A_V=5.2+/-0.8mag, 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. Relative flux calibration of the bands was achieved using photometry from the NACO imaging data. 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-Beta emission in the J-band, accretion is probably still ongoing onto the CT Cha companion. From temperature and luminosity (log(Lbol/Lsun)= -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 MJup 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.
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