Diborane (B(2)H(6)), a high energy density material, was believed to be stable in a wide P, T interval. A systematic investigation of the B-H system using the ab initio variable-composition evolutionary simulations shows that boron monohydride (BH) is thermodynamically stable and can coexist with solid B, H(2), and B(2)H(6) in a wide pressure range above 50 GPa. B(2)H(6) becomes unstable and decomposes into the Ibam phase of BH and H(2) (C2/c) at 153 GPa. The semiconducting layered Ibam structure of BH at 168 GPa transforms into a metallic phase with space group P6/mmm and a 3D topology with strong B-B and B-H covalent bonds. The Ibam-P6/mmm transformation pathway suggests the possibility of obtaining the metastable Pbcm phase on cold decompression of the P6/mmm phase. The electron-phonon coupling calculations indicate that P6/mmm-BH is a phonon-mediated superconductor with a critical temperature of superconductivity (T(c)) of 14.1-21.4 K at 175 GPa.