In this paper we explore the feasibility of predicting an underwater acoustic (UWA) channel impulse response one travel time ahead. Our work is motivated by the design of UWA communication systems that will employ adaptive modulation, whose performance relies on the ability to predict the channel up to a few seconds into the future. The possibility of predicting the channel response is demonstrated using real data collected during an experiment conducted in shallow water off the western coast of Kauai, Hawaii, in June 2008. The key to enabling prediction is decoupling of the effects of motion-induced phase offset from the more slowly varying channel path gains. It is shown that a significant performance improvement can be achieved using prediction as compared to using outdated channel estimates.