A sync of the type you describe is something that is planned for the future.
CHM is not a Calibre supported format. I also do not know if there are any ebook readers that support cdhm as a native format. I believe there are a variety of tools that claim to be able to convert CHM files to HTML (which is a Calibre supported format) which can then be converted to a format your ebook reader understands. I do not have much experience of these tools so do not know which to recommend. I tried the ABC converter but was not very impressed by the results.