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When social chatbots make mistakes, and they do, how they recover determines whether users trust them again. Social chatbots are increasingly integrated into everyday life, yet they remain prone to generating convincing but inaccurate information. The social connection they build with users makes such errors particularly consequential. We conducted a between-subjects experiment (N=120) comparing three error correction strategies: a webpage retraction, self-correction by the same social chatbot, and correction by an expert chatbot. Our results reveal two key findings. First, all three strategies corrected the error equally well, but only self-correction did so without damaging the chatbot's credibility: participants rated self-correcting chatbots significantly higher in both trustworthiness and perceived expertise than chatbots whose errors were corrected by external sources. Second, the strength of the user's social connection with the chatbot, measured through social attraction and self-disclosure, significantly predicted the magnitude of belief change, but only when the chatbot corrected itself. Outsourcing corrections to an external source severed this link entirely. These findings suggest that social chatbots should correct their own mistakes rather than outsource corrections, and that investing in social connection is a functional mechanism that amplifies correction effectiveness, not merely a design feature. We discuss implications for designing chatbots that maintain long-term credibility while effectively addressing their own errors.