Prompting Large Language Models (LLMs) has created new and interesting means for classifying textual data. While evaluating and remediating group fairness is a well-studied problem in classifier fairness literature, some classical approaches (e.g., regularization) do not carry over, and some new opportunities arise (e.g., prompt-based remediation). We measure fairness of LLM-based classifiers on a toxicity classification task, and empirically show that prompt-based classifiers may lead to unfair decisions. We introduce several remediation techniques and benchmark their fairness and performance trade-offs. We hope our work encourages more research on group fairness in LLM-based classifiers.