We present VLT/NACO SDI images of the very nearby star SCR 1845-6357 (hereafter SCR 1845). SCR 1845 is a recently discovered (Hambly et al. 2004) M8.5 star just 3.85 pc from the sun (Henry et al. 2006). Using the capabilities of the unique SDI device, we discovered a substellar companion to SCR 1845 at a separation of 4.5 AU (1.170+-0.003 on the sky) and fainter by 3.57+-0.057 mag in the 1.575 um SDI filter. This substellar companion has an H magnitude of 13.16+0.31-0.26 (absolute H magnitude of 15.30+0.31-0.26), making it likely the brightest mid-T dwarf known. The unique Simultaneous Differential Imager (SDI) consists of 3 narrowband filters placed around the 1.6 um methane absorption feature characteristic of T-dwarfs (Teff < 1200 K). The flux of the substellar companion drops by a factor of 2.7+-0.1 between the SDI F1(1.575 um) filter and the SDI F3(1.625 um) filter, consistent with strong methane absorption in a substellar companion. We estimate a spectral type of T5.5+-1 for the companion based on the strength of this methane break. The chances that this object is a background T dwarf are vanishing small -- and there is no isolated background T-dwarf in this part of the sky according to 2MASS. Thus, it is a bound companion, hereafter SCR 1845-6357B. For an age range of 100 Myr - 10 Gyr and spectral type range of T4.5-T6.5, we find a mass range of 9 - 65 MJup for SCR 1845B from the Baraffe et al. 2003 COND models. SCR 1845AB is the 24th closest stellar system to the Sun (at 3.85 pc); the only brown dwarf system closer to the Sun is Eps Indi Ba-Bb (at 3.626 pc). In addition, this is the first T-dwarf companion discovered around a low mass star.
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