The transfer of information between different physical forms-for example processing entities and memory-is a central theme in communication and computation. This is crucial in quantum computation, where great effort must be taken to protect the integrity of a fragile quantum bit (qubit). However, transfer of quantum information is particularly challenging, as the process must remain coherent at all times to preserve the quantum nature of the information. Here we demonstrate the coherent transfer of a superposition state in an electron-spin `processing' qubit to a nuclear-spin `memory' qubit, using a combination of microwave and radio-frequency pulses applied to 31P donors in an isotopically pure 28Si crystal. The state is left in the nuclear spin on a timescale that is long compared with the electron decoherence time, and is then coherently transferred back to the electron spin, thus demonstrating the 31P nuclear spin as a solid-state quantum memory. The overall store-readout fidelity is about 90 per cent, with the loss attributed to imperfect rotations, and can be improved through the use of composite pulses. The coherence lifetime of the quantum memory element at 5.5K exceeds 1s.