Optical isomerism is exhibited by only those complexes in which elements of symmetry are absent. Octahedral complexes of the types $\left[\mathrm{M}(\mathrm{aa})_3\right],\left[\mathrm{M}(\mathrm{aa}) \mathrm{x}_2, \mathrm{y}_2\right]$ and $\left[\mathrm{M}(\mathrm{aa})_2 \mathrm{x}_2\right]$ have absence of elements of symmetry, thus exhibit optical isomerism. Here, $a a$ represents bidentate ligand, $x$ or $y$ represents monodentate ligand and $M$ represents central metal ion.
Hence, $\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_3 \mathrm{Cl}_3\right]^0$ due to presence of symmetry elements does not exhibit optical isomerism.