The concept of consciousness existing outside the body (e.g. near-death and out-of body experiences, NDE/OBEs, or after death, indicative of a ‘soul’) is a staple of religious traditions, but shunned by conventional science because of an apparent lack of rational explanation. However conventional science based entirely on classical physics cannot account for normal in-the-brain consciousness. The Penrose-Hameroff ‘Orch OR’ model is a quantum approach to consciousness, connecting brain processes (microtubule quantum computations inside neurons) to fluctuations in fundamental spacetime geometry, the fine scale structure of the universe. Recent evidence for significant quantum coherence in warm biological systems, scale-free dynamics and end-of-life brain activity support the notion of a quantum basis for consciousness which could conceivably exist independent of biology in various scalar planes in spacetime geometry. Sir Roger Penrose does not necessarily endorse such proposals which relate to his ideas in physics. Based on Orch OR, we offer a scientific hypothesis for a ‘quantum soul’.