In the pop-up window that appears, select Allow offline docs. You will see a prompt to install the Google Docs extension from the Chrome Web Store. Your offline docs will then download to your PC automatically.
You must authorize offline access for each computer. To access your offline docs, just visit docs.google.com as you normally would. A lightning-bolt icon appears next to the Docs logo to let you know when you are working offline.
Even though you can only view your documents offline, you can copy any document that is available to you offline; as a workaround, you might copy and paste your document into a desktop editor. Or, since you're using Chrome, you might try an offline text editor that works right in your browser, such as Writebox or Write Space. Both apps let you work on one set of text at a time, and both automatically save your work so you can paste it back into Google Docs when you get back online.
This approach is not ideal for a collaborative document, but at least it's an option if you need to work offline in a pinch. And Google may come up with its own native Docs solution for this problem or any of the other annoyances.