GPT-4V's purported strong multimodal abilities raise interests in using it to automate radiology report writing, but there lacks thorough evaluations. In this work, we perform a systematic evaluation of GPT-4V in generating radiology reports on two chest X-ray report datasets: MIMIC-CXR and IU X-Ray. We attempt to directly generate reports using GPT-4V through different prompting strategies and find that it fails terribly in both lexical metrics and clinical efficacy metrics. To understand the low performance, we decompose the task into two steps: 1) the medical image reasoning step of predicting medical condition labels from images; and 2) the report synthesis step of generating reports from (groundtruth) conditions. We show that GPT-4V's performance in image reasoning is consistently low across different prompts. In fact, the distributions of model-predicted labels remain constant regardless of which groundtruth conditions are present on the image, suggesting that the model is not interpreting chest X-rays meaningfully. Even when given groundtruth conditions in report synthesis, its generated reports are less correct and less natural-sounding than a finetuned LLaMA-2. Altogether, our findings cast doubt on the viability of using GPT-4V in a radiology workflow.