We present a method for creating a quantum degenerate gas of metastable alkaline-earth-metal atoms. This has yet to be achieved due to inelastic collisions that limit evaporative cooling in the metastable states. Quantum degenerate samples prepared in the S-1(0) ground state can be rapidly transferred to either the P-3(2) or P-3(0) state via a coherent three-photon process. Numerical integration of the density-matrix evolution for the fine structure of bosonic alkaline-earth-metal atoms shows that transfer efficiencies of similar or equal to 90% can be achieved with experimentally feasible laser parameters in both Sr and Yb. Importantly, the three-photon process can be set up such that it imparts no net momentum to the degenerate gas during the excitation, which will allow for studies of metastable samples outside the Lamb-Dicke regime. We discuss several experimental challenges to successfully realizing our scheme, including the minimization of differential ac Stark shifts between the four states connected by the three-photon transition.