Newborns are able to neurally discriminate between speech and nonspeech right after birth. To date it remains unknown whether this early speech discrimination and the underlying neural language network is associated with later language development. Preterm-born children are an interesting cohort to investigate this relationship, as previous studies have shown that preterm-born neonates exhibit alterations of speech processing and have a greater risk of later language deficits. This investigation also holds clinical importance, as differences in neonatal speech discrimination and its functional networks may serve as predictors of later language outcomes. We therefore investigated neural speech discrimination using functional near-infrared spectroscopy in 92 preterm- and term-born neonates and its predictive value for language development in 45 of them. Three to five years later, preterm-born and term-born children did not significantly differ in language comprehension, sentence production, the use of morphological rules, or phonological short-term memory. In addition, the gestational age at birth was not a significant predictor of language development. Neural speech discrimination, in contrast, was strongly correlated with later phonological short-term memory. However, not the extent of speech discrimination, but rather its lateralization, was a predictor of language development. Children with less right hemisphere involvement--and therefore more left-lateralized speech discrimination at birth--showed better development of phonological short-term memory three to five years later. These findings suggest that the ability of fetuses to form memory traces is reflected by neonatal abilities to neurally discriminate speech, which in turn is a predictor for later phonological short-term memory.