The answer to this question depends on the structure of your document. If it can be structured as a series of short, unbreakable sections, then you're in luck! There is a Chrome-compatible way to simulate running page headers in this type of document (actually, it works in all of the popular desktop browsers).
The basic idea is to put a copy of the header at the top of each unbreakable section, and then use a negative margin to hide the copy so that it will only be seen if a page break bumps the section to the next page. That's a bit of an oversimplification, though, so I would recommend studying the code below before trying this on your own documents.
Test doc:
Unbreakable section.
Unbreakable section.
Unbreakable section.
Unbreakable section.
Unbreakable section.
Unbreakable section.
Unbreakable section.
Unbreakable section.
Unbreakable section.
Unbreakable section.
Unbreakable section.
Unbreakable section.
Unbreakable section.
Unbreakable section.
Unbreakable section.
Unbreakable section.
Unbreakable section.
Unbreakable section.
Unbreakable section.
Unbreakable section.
Unbreakable section.
Unbreakable section.
Unbreakable section.
Unbreakable section.
Unbreakable section.
Unbreakable section.
Unbreakable section.
Unbreakable section.
Unbreakable section.
Unbreakable section.
Unbreakable section.
Unbreakable section.
Unbreakable section.
Unbreakable section.
Unbreakable section.
Unbreakable section.
Unbreakable section.
Unbreakable section.
Unbreakable section.
Unbreakable section.
Unbreakable section.
Unbreakable section.
Unbreakable section.
Unbreakable section.
Unbreakable section.
Unbreakable section.
Unbreakable section.
Unbreakable section.
Unbreakable section.
You wouldn't want to use this technique in documents that have blocks of text larger than about 1/3 of a page, but it works great for docs that consist of small, discrete sections, such as forms and tables.
My answer to this other post might also be of interest. It shows how to create Chrome-compatible repeating table headers using the same basic principles, but all the extra markup is added via javascript so that it doesn't "pollute" the original HTML doc.
