Many existing chatbots do not effectively support mixed initiative, forcing their users to either respond passively or lead constantly. We seek to improve this experience by introducing new mechanisms to encourage user initiative in social chatbot conversations. Since user initiative in this setting is distinct from initiative in human-human or task-oriented dialogue, we first propose a new definition that accounts for the unique behaviors users take in this context. Drawing from linguistics, we propose three mechanisms to promote user initiative: back-channeling, personal disclosure, and replacing questions with statements. We show that simple automatic metrics of utterance length, number of noun phrases, and diversity of user responses correlate with human judgement of initiative. Finally, we use these metrics to suggest that these strategies do result in statistically significant increases in user initiative, where frequent, but not excessive, back-channeling is the most effective strategy.