An ab initio potential-energy surface for the ground doublet state of BH3+ has been constructed at the QCISD(T)/6-311G(d,p) level of theory. Classical simulations of the collision between BH+ and H-2(D-2) and isotopic analogs show that the deep BH3+ well gives rise to substantial "scrambling" of the hydrogen and deuterium atoms leading to BHD+ + D, BD+ + HD, and BD2+ + H products.