The atomic structure and electronic properties of various defects consisting of B and C atoms in Si predoped with C impurities are investigated through first-principles density-functional calculations. In the absence of Si self-interstitials ($I_s$), substitutional B and C atoms interact repulsively with each other, implying that B-C pairs at neighboring substitutional sites do not play a role in the retardation of B diffusion. After examining various configurations for a $I_s-B-C$ complex, which can be formed in the excess of self-interstitials, it is found that a C-B split-interstitial, where the B and C atoms share a single lattice site along the  axis, is the most stable defect. For several diffusion pathways, along which the B dopant diffuses from the C-B split-interstitial complex with  orientation to nearby tetrahedral and hexagonal sites, very high migration energies of about 3 eV are calculated, which indicate that the diffusing B atom can be easily trapped in the neighborhood of C. The range of the C trap potential is estimated to be about 7 $\AA$. These results suggest that the suppression of B diffusivity in the presence of C is attributed to the formation of C-B split-interstitial complexes, in addition to the reduction of self-interstitials, which are available for B diffusion.