The heats of formation of BH, BH2, BH3, and B2H6 have been obtained from ab initio coupled cluster calculations by using a systematic sequence of correlation consistent Gaussian basis sets. The best values were obtained by extrapolating the finite basis set results to the complete basis set limit and by incorporating an estimate of core/valence correlation effects. In general, the largest calculations in this study utilized quadruple-zeta-level basis sets that were augmented by an additional shell of diffuse functions. Even larger basis set calculations were performed on the smallest of the four systems in order to test the accuracy of the complete basis set extrapolation. Vibrational zero point energies were taken from experiment when available. Missing values were replaced by theoretical harmonic frequencies scaled to more closely approximate the experimental values. The calculated heats of formation are Delta HOf0(BH) = 106.2 +/- 0.3 kcal/mol, Delta H-f(0)(BH2) = 78.4 +/- 0.6 kcal/mol, Delta H-f(0)(BH3) = 25.8 +/-0.7 kcal/mol, and Delta H-f(0)(B2H6) = 13.7 +/- 1.4 kcal/mol.