We show that the local density approximation (LDA) of the density functional theory (DFT) fails to describe the nature of the shallow boron acceptor state B-Si: like the well known underestimation of the fundamental band gap, the localization of this defect state is also strongly underestimated. Upon application a self-consistent correction to the band gap a pronouced Jahn-Teller distortion towards C-1h-symmetry occurs. As a result, the calculated hyperfine interaction with one prominent C-13-ligand, strongly underestimated before, are in good agreement with experimental data.