The natural linear-scaled coupled-cluster (NLSCC) method (Flocke, N.; Bartlett, R. J. J. Chem. Phys. 2004, 121, 10935),is extended to include approximate triple excitations via a coupled-cluster with single, double, and triple excitation method (CCSDT-3). The triples contribution can potentially be embedded in a larger singles and doubles region. NLSCC exploits the extensivity of the CC wave function to represent it in terms of transferable natural localized molecular orbitals (NLMOs) or functional groups thereof that are obtained from small quantum mechanical (QM) regions. Both occupied and virtual NLMOs are local because they derive from the single-particle density matrix. Noncanonical triples amplitudes are avoided by applying the unitary localization matrix to the canonical CC wave function for a QM region. A generalized NLMO code interfaced to the ACES 11 quantum chemistry software package provides NLMOs for the relevant number of atoms in a given functional group. Applications include linear polyglycine and the pentapeptide met-enkephalin, which was chosen as a more realistic three-dimensional system with nontrivial side chains. The results show that the triples contributions are quite large for aromatic bonds suggesting an interesting active space method for triples in which different bonds require different excitation levels. The NLSCC approach recovers a very large percentage (> 99%) of the CCSD or CCSDT-3 correlation energy.