Hearing is operational from the third trimester of gestation. Infants thus first experience language in the womb. In this talk I will present a series of near-infrared spectroscopy experiments with newborns suggesting that this prenatal experience may already shape how infants perceive and start learning about language. As maternal tissues act as low-pass filters, fetuses mainly experience the prosody of speech, fine details necessary for the identification of words are mostly suppressed. I will show that at birth infants already recognize the prosodic properties of the language(s) they heard in utero, they weigh prosody as a strong cue to package the speech stream into relevant units. I will link this early prosodic experience to theories of prosodic bootstrapping assumed to operate later during language acquisition.