A six-dimensional potential energy surface (PES) for the adiabatic ground electronic state has been developed and quasiclassical trajectory calculations (QCT), focusing on selectivity of vibrational and rotational initial states upon reactive cross sections, have been performed for the title reaction BO + H-2 --> HBO + H. It constitutes the first dynamical study of this four-atom reaction, for which the specified reaction channel is the only one open at moderate energies, the HOB + H channel being open at an energy of 55 kcal/mol above reactants. An analytical PES has been developed based on a Sorbie-Murrell many-body expansion, giving rise to a monovalued, smooth function which correctly reproduces the most important features of the interaction potential. Extended QCT calculations have been performed for low and moderate collision energies, which have led to a proper characterization of the excitation function shape. Additional extended calculations covered several vibrational and rotational initial states, so that selectivity upon reactivity has been studied in detail. Noteworthy features are the clear enhancement of the reactive cross section as the H-2 vibration is increased and the inhibition of the reactivity as the BO vibrational energy is higher, which have been interpreted in terms of the characteristics of the transition state normal models) correlating with the corresponding asymptotic states. It has been also found that several dynamical features are easily explained as a consequence of the collinearity of the transition state.