The local coupled cluster method DLPNO-CCSD(T) allows calculations on systems containing hundreds of atoms to be performed while typically reproducing canonical CCSD(T) energies with chemical accuracy. In this work, we present a scheme for decomposing the DLPNO-CCSD(T) interaction energy between two molecules into physical meaningful contributions, providing a quantification of the most important components of the chemical interaction. The method, called Local Energy Decomposition (LED), is straightforward and requires negligible additional computing time. Both the Hartree-Fock and the correlation energy are decomposed into contributions from localized or pairs of localized occupied orbitals. Assigning these localized orbitals to fragments allows one to differentiate between intra- and intermolecular contributions to the interaction energy. Accordingly, the interaction energy can be decomposed into electronic promotion, electrostatic, exchange, dynamic charge polarization, and dispersion contributions. The LED scheme is applied to a number of test cases ranging from weakly, dispersively bound complexes to systems with strong ionic interactions. The dependence of the results on the one-particle basis set and various technical aspects, such as the localization scheme, are carefully studied in order to ensure that the results do not suffer from technical artifacts. A numerical comparison between the DLPNO-CCSD(T)/LED and the popular symmetry adapted perturbation theory (DFT-SAPT) is made, and the limitations of the proposed scheme are discussed.