Abstract: Using a combination of random configuration sampling, molecular dynamics simulated annealing with empirical potential, and ensuing structural refinement by first-principles density functional calculations, we perform an extensive ground-state search for the most stable configurations of small carbon interstitial clusters in SiC. Our search reveals a "magic" cluster number of three atoms, where the formation energy per interstitial shows a distinct minimum. A carbon tri-interstitial cluster with trigonal C_3v symmetry is discovered, in which all carbon atoms are fourfold coordinated. In addition to its special thermodynamic stability, its localized vibrational modes are also in a very good agreement with the experimental photoluminescence spectra of the D_II center in both 3C- and 4H-SiC. The D_II center is one of the most persistent defects in SiC, and we propose that the discovered carbon tri-interstitial is responsible for this center.