This article presents a new theory about the origin of REM sleep. REM is an integral part of the human sleep cycle and the neurological substrate most consistently associated with dreams and dream recall. According to this thesis, REM sleep evolved out of a primordial defensive reflex: tonic immobility. This reflex, sometimes also called death-feigning or animal hypnosis, is usually the last line of defense against an attacking predator. Tonic immobility, common in both vertebrates and invertebrates, has a number of neuroanatomical and behavioral attributes that overlap with those of REM sleep. This overlap is suggestive of an evolutionary kinship. The article presents conceptual arguments and empirical facts in support of this relationship.