Like text, programs have styles, and certain programming styles are more desirable than others for program readability, maintainability, and performance. Code style transfer, however, is difficult to automate except for trivial style guidelines such as limits on line length. Inspired by the success of using language models for text style transfer, we investigate if code language models can perform code style transfer. Code style transfer, unlike text transfer, has rigorous requirements: the system needs to identify lines of code to change, change them correctly, and leave the rest of the program untouched. We designed CSB (Code Style Benchmark), a benchmark suite of code style transfer tasks across five categories including converting for-loops to list comprehensions, eliminating duplication in code, adding decorators to methods, etc. We then used these tests to see if large pre-trained code language models or fine-tuned models perform style transfer correctly, based on rigorous metrics to test that the transfer did occur, and the code still passes functional tests. Surprisingly, language models failed to perform all of the tasks, suggesting that they perform poorly on tasks that require code understanding. We will make available the large-scale corpora to help the community build better code models.