The recently developed local pair natural orbital coupled cluster theory with single and double excitations (LPNO-CCSD) was used to study the rhodium-catalyzed asymmetric hydrogenation of two prochiral enamides. The method was carefully calibrated with respect to its accuracy. According to calculations on a truncated model system, the effects of perturbative triples (T) on the reaction energetics are very limited, the LPNO approximation is accurate, and complete basis set extrapolation (CBS) causes only minor changes in the relative energies computed with a standard basis set (def2-TZVP). The results for the full system are thus believed to be within 1-2 kcal/mol of the CCSD(T)/CBS limit for the present systems. Relativistic effects were treated by a scalar relativistic Hamiltonian using the zeroth order regular approximation (ZORA). The results of the study were compared to density functional calculations on the same systems and with calculations available in the literature. All calculations predict the correct stereochemical outcome of the reaction that is determined by the relative energies of the transition states in the early stages of the catalytic cycle. In general, DFT calculations using the B3LYP functional are in reasonable agreement with the LPNO-CCSD results, although deviations of 3-5 kcal/mol exist that are also not entirely systematic in the minor and major reaction branches. The present case study thus demonstrates that catalytic reactions, which are well described by single-reference electronic structure theory, can now be routinely studied with confidence in systems with 50-100 atoms applying local correlation methods that are as easy to use as DFT methods.