Introduction: Early language development in infants is being increasingly studied, though only recently with direct measurements of brain activity rather than with behavioral or physiological measurements. In the current study, we use electroencephalographic (EEG) recordings of 2-week-old infants to look for signs of prenatal learning and to investigate newborns' abilities to process language. We also look at the influence of prenatal stress factors and at the predictive value of the newborns' language processing abilities for later language development. Methods: Sixty pregnant women played a rhyme to their abdomen twice a day from the 34th week of pregnancy until birth, to familiarize the fetus with the rhyme. At around 2 weeks after delivery (mean age 16 days), the newborns were exposed to the familiar rhyme as well as to an unfamiliar one while their EEG was recorded. Additionally, three manipulations of the familiar rhyme were played: (1) low-pass filtered, (2) with changed rhythm, and (3) inverted and played backwards. The data was analyzed to see how well the infant brain signal followed the speech envelope in each condition. Accounting for the heterogenous approach used for neural speech tracking in the literature, we used four methods, namely: (1) coherence, (2) Hilbert coherence, (3) temporal response functions (TRF), and (4) mutual information (MI). The maternal prenatal depression was evaluated with Edinburgh Prenatal Depression Score and the chronic fetal stress was measured from the hair cortisol levels of the 2 week-olds. The language development at 6 months of age was evaluated with the Bayley Scales. Results and discussion: Overall, the results indicate the presence of prenatal learning, with the unfamiliar rhyme eliciting stronger cortical tracking (higher coherence and MI) than the familiar rhyme, which suggests stronger brain-to-speech coupling for the unfamiliar rhyme, perhaps deriving from more effort to process the unexpected stimulus. However, the original version of the familiar rhyme proved to be the easiest to track compared to the language- and rhythm-manipulations, (higher MI for the original rhyme than the language manipulation and higher coherence and mTRF correlation coefficients for the original rhyme than the rhythm manipulation). This indicates language discrimination and a prosodic-based learning of the familiar rhyme. Furthermore, there is an indication of phonotactic sensitivity at this young age, with less tracking (lower Hilbert coherence and lower mTRF correlation coefficients) of the low-pass filtered rhyme than the original version, indicating that the phonological cues erased by the filtering were important for the newborn's ability to follow the rhyme. Furthermore, the mothers' depression scores positively correlated with the infant's tracking ability for the familiar rhyme. This suggests that a slightly lower mood was more stimulative for the fetal language development. The chronic fetal stress levels, however, were negatively correlated with the cortical tracking abilities. Importantly, the newborn's cortical tracking was positively correlated with the infant's language development at 6 months of age, underlining the predictive value of the early assessment of language processing. Conclusion: Prenatal learning is well established, but evidence including (healthy) brain data in the first weeks of life is scarce. The current study shows that newborns can discriminate between a familiar and unfamiliar rhyme, while also highlighting the role of prosody in early language processing, and bringing new evidence of their sensitivity to phonotactic cues in auditory stimuli. Furthermore, the newborn's ability to track a rhyme is correlated with their language development at 6 months. The newborn's cortical tracking of the familiar rhyme is further increased by moderately low maternal mood, but decreased by fetal stress. Future studies with similar fine-grained linguistic designs but of older infants should teach us the timeline of what exactly is learned prenatally and at very early age in respect to language.