The development of speech perception shows a dramatic transition between infancy and adulthood. Between 6 and 12 months, infants' initial ability to discriminate all phonetic units across the world's languages narrows-native discrimination increases while non-native discrimination shows a steep decline. We used magnetoencephalography (MEG) to examine whether brain oscillations in the theta band (4-8 Hz), reflecting increases in attention and cognitive effort, would provide a neural measure of the perceptual narrowing phenomenon in speech. Using an oddball paradigm, we varied speech stimuli in two dimensions, stimulus frequency (frequent vs. infrequent) and language (native vs. non-native speech syllables) and tested 6-month-old infants, 12-month-old infants, and adults. We hypothesized that 6-month-old infants would show increased relative theta power (RTP) for frequent syllables, regardless of their status as native or non-native syllables, reflecting young infants' attention and cognitive effort in response to highly frequent stimuli ("statistical learning"). In adults, we hypothesized increased RTP for non-native stimuli, regardless of their presentation frequency, reflecting increased cognitive effort for non-native phonetic categories. The 12-month-old infants were expected to show a pattern in transition, but one more similar to adults than to 6-month-old infants. The MEG brain rhythm results supported these hypotheses. We suggest that perceptual narrowing in speech perception is governed by an implicit learning process. This learning process involves an implicit shift in attention from frequent events (infants) to learned categories (adults). Theta brain oscillatory activity may provide an index of perceptual narrowing beyond speech, and would offer a test of whether the early speech learning process is governed by domain-general or domain-specific processes.