Background: During sleep animals are relatively unresponsive and unaware of their environment, and therefore, more exposed to predation risk than alert and awake animals. This vulnerability might influence when, where and how animals sleep depending on the risk of predation perceived before going to sleep. Less clear is whether animals remain sensitive to predation cues when already asleep. Methodology/Principal Findings: We experimentally tested whether great tits are able to detect the chemical cues of a common nocturnal predator while sleeping. We predicted that birds exposed to the scent of a mammalian predator (mustelid) twice during the night would not go into torpor (which reduces their vigilance) and hence would not reduce their body temperature as much as control birds, exposed to the scent of another mammal that does not represent a danger for the birds (rabbit). As a consequence of the higher body temperature birds exposed to the scent of a predator are predicted to have a higher resting metabolic rate (RMR) and to lose more body mass. In the experiment, all birds decreased their body temperature during the night, but we did not find any influence of the treatment on body temperature, RMR, or body mass. Conclusions/Significance: Our results suggest that birds are not able to detect predator chemical cues while sleeping. As a consequence, antipredatory strategies taken before sleep, such as roosting sites inspection, may be crucial to cope with the vulnerability to predation risk while sleeping.