What is it like to be invisible? This question has long fascinated man and has been the central theme of many classic literary works. Recent advances in materials science suggest that invisibility cloaking of the human body may be possible in the not-so-distant future. However, it remains unknown how invisibility affects body perception and embodied cognition. To address these questions, we developed a perceptual illusion of having an entire invisible body. Through a series of experiments, we characterized the multisensory rules that govern the elicitation of the illusion and show that the experience of having an invisible body reduces the social anxiety response to standing in front of an audience. This study provides an experimental model of what it is like to be invisible and shows that this experience affects bodily self-perception and social cognition.