We propose a quantum repeater protocol which builds on the well-known DLCZ protocol [L.M. Duan, M.D. Lukin, J.I. Cirac, and P. Zoller, Nature 414, 413 (2001)], but which uses photon pair sources in combination with memories that allow to store a large number of temporal modes. We suggest to realize such multi-mode memories based on the principle of photon echo, using solids doped with rare-earth ions. The use of multi-mode memories promises a speedup in entanglement generation by several orders of magnitude and a significant reduction in stability requirements compared to the DLCZ protocol.