Here we report, for the first time, a relationship between sensitivity to amplitude envelope rise time in infants and their later vocabulary development. Recent research in auditory neuroscience has revealed that amplitude envelope rise time plays a mechanistic role in speech encoding. Accordingly, individual differences in infant discrimination of amplitude envelope rise times could be expected to relate to individual differences in language acquisition. A group of 50 infants taking part in a longitudinal study contributed rise time discrimination thresholds when aged 7 and 10 months, and their vocabulary development was measured at 3 years. Experimental measures of phonological sensitivity were also administered at 3 years. Linear mixed effect models taking rise time sensitivity as the dependent variable, and controlling for non-verbal IQ, showed significant predictive effects for vocabulary at 3 years, but not for the phonological sensitivity measures. The significant longitudinal relationship between amplitude envelope rise time discrimination and vocabulary development suggests that early rise time discrimination abilities have an impact on speech processing by infants.