Bulk single crystals of the ternary intermetallic compounds CeNi2Si2, CePd2Si2 and CePt2Si2 have been grown from the melt with a modified "tri-arc" Czochralski method. The as-grown crystals were characterized by X-ray, microprobe, and chemical analyses. The measured densities were compared with the calculated densities as obtained from the lattice parameters. In all as-grown single crystals no detectable precipitates of foreign phases were observed. These precipitates are always present in polycrystalline samples, even after a heat-treatment, and are visible on the grain boundaries and in the subgrain structure.