A full configuration interaction study on the BH molecule is presented. The potential energy curves of 20 different electronic states have been calculated correlating the four valence electrons. On the two most important states, i.e. the X1Sigma+ and A1Pi states, a complete study has been performed. This includes the effect of core electron correlation, estimated via truncated configuration interaction techniques. The dissociation energy of the molecule in the two states and the height of the predissociative barrier in the A1Pi state have been determined with basis sets of increasing quality.