The ability to discriminate the trajectories of moving objects is highly adaptive and fundamental for physical and social interactions. Therefore, we could reasonably expect sensitivity to different trajectories already at birth, as a precursor of later communicative and defensive abilities. To investigate this possibility, we measured newborns' looking behavior to evaluate their ability to discriminate between visual stimuli depicting motion along different trajectories happening within the space surrounding their body. Differently from previous studies, we did not take into account defensive reactions, which may not be elicited by impending collision as newborns might not categorize approaching stimuli as possible dangers. In two experiments, we showed that newborns display a spontaneous visual preference for trajectories directed toward their body. We found this visual preference when visual stimuli depicted motion in opposite directions (approaching vs. receding) as well as when they both moved toward the peripersonal space and differed only in their specific target (i.e., the body vs. the space around it). These findings suggest that at birth human infants seem to be already equipped with visual mechanisms predisposing them to perceive their presence in the environment and to adaptively focus their attention on the peripersonal space and their bodily self.