Social robots aim to establish long-term bonds with humans through engaging conversation. However, traditional conversational approaches, reliant on scripted interactions, often fall short in maintaining engaging conversations. This paper addresses this limitation by integrating large language models (LLMs) into social robots to achieve more dynamic and expressive conversations. We introduce a fully-automated conversation system that leverages LLMs to generate robot responses with expressive behaviors, congruent with the robot's personality. We incorporate robot behavior with two modalities: 1) a text-to-speech (TTS) engine capable of various delivery styles, and 2) a library of physical actions for the robot. We develop a custom, state-of-the-art emotion recognition model to dynamically select the robot's tone of voice and utilize emojis from LLM output as cues for generating robot actions. A demo of our system is available here. To illuminate design and implementation issues, we conduct a pilot study where volunteers chat with a social robot using our proposed system, and we analyze their feedback, conducting a rigorous error analysis of chat transcripts. Feedback was overwhelmingly positive, with participants commenting on the robot's empathy, helpfulness, naturalness, and entertainment. Most negative feedback was due to automatic speech recognition (ASR) errors which had limited impact on conversations. However, we observed a small class of errors, such as the LLM repeating itself or hallucinating fictitious information and human responses, that have the potential to derail conversations, raising important issues for LLM application.