Recent large language models (LLMs) have demonstrated a remarkable ability to perform natural language understanding and generation tasks. In this work, we investigate the use of LLMs for evaluating faithfulness in news summarization, finding that it achieves a strong correlation with human judgments. We further investigate LLMs' capabilities as a faithfulness post-editor, experimenting with different chain-of-thought prompts for locating and correcting factual inconsistencies between a generated summary and the source news document and are able to achieve a higher editing success rate than was reported in prior work. We perform both automated and human evaluations of the post-edited summaries, finding that prompting LLMs using chain-of-thought reasoning about factual error types is an effective faithfulness post-editing strategy, performing comparably to fine-tuned post-editing models. We also demonstrate that multiple rounds of post-editing, which has not previously been explored, can be used to gradually improve the faithfulness of summaries whose errors cannot be fully corrected in a single round.