A long-lived quantum memory is a firm requirement for implementing a quantum repeater scheme. Recent progress in solid-state rare-earth-ion-doped systems justifies their status as very strong candidates for such systems. Nonetheless an optical memory based on spin-wave storage at the single-photon level has not been shown in such a system to date, which is crucial for achieving the long storage times required for quantum repeaters. In this paper we show that it is possible to execute a complete atomic frequency comb (AFC) scheme, including spin-wave storage, with weak coherent pulses of n¯¯=2.5±0.6 photons per pulse. We discuss in detail the experimental steps required to obtain this result and demonstrate the coherence of a stored time-bin pulse. We show a noise level of (7.1±2.3)×10−3 photons per mode during storage, and this relatively low noise level paves the way for future quantum optics experiments using spin waves in rare-earth-doped crystals.