The sensory input that we encounter while navigating through each day is highly structured, containing patterns that repeat over time. Statistical learning is the process of becoming attuned to these patterns and can facilitate online processing. These online facilitation effects are often ascribed to prediction, in which information about an upcoming event is represented before it occurs. However, previously observed facilitation effects could also be due to retrospective processing. Here, using a speech-based segmentation paradigm, we tested whether statistical learning leads to the prediction of upcoming syllables. Specifically, we probed for a behavioural hallmark of genuine prediction, in which a given prediction benefits online processing when confirmed, but incurs costs if disconfirmed. In line with the idea that prediction is a key outcome of statistical learning, we found a trade-off in which a greater benefit for processing predictable syllables was associated with a greater cost in processing syllables that occurred in a "mismatch" context, outside of their expected positions. This trade-off in making predictions was evident at both the participant and the item (i.e., individual syllable) level. Further, we found that prediction did not emerge indiscriminately to all syllables in the input stream, but was deployed selectively according to the trial-by-trial demands of the task. Explicit knowledge of a given word was not required for prediction to occur, suggesting that prediction operates largely implicitly. Overall, these results provide novel behavioural evidence that prediction arises as a natural consequence of statistical learning.