Observed frequently in human-human interactions, entrainment is a social phenomenon in which speakers become more like each other over the course of a conversation. Acoustic-prosodic entrainment occurs when individuals adapt their acoustic-prosodic speech features, such as pitch and intensity. Correlated with communicative success, naturalness, and conversational flow as well as social variables such as rapport, a dialogue system which automatically entrains has the potential to improve verbal interactions by increasing rapport, naturalness, and conversational flow. In an application like the learning companion, such a socially responsive dialogue system may improve learning and motivation. However, it is not clear how to produce entrainment in an automatic dialogue system in ways that produce the effects seen in human-human dialogue. In this paper, we take the first steps towards implementing a spoken dialogue system which can entrain. We propose three methods of pitch adaptation based on analysis of human entrainment, and design and implement a system which can manipulate the pitch of text-to-speech output adaptively. We find a clear relationship between perceptions of rapport and different forms of pitch adaptations. Certain adaptations are perceived as significantly more natural and rapport-like. Ultimately, adapting by shifting the pitch contour of the text-to-speech output by the mean pitch of the user results in the highest reported measures of rapport and naturalness.