Current Answer, Posted On June 22nd 2022

According to a comment by Paul Watson, the ability to git clone GitBook repositories has either been removed or moved to a different URL.

When I logged into gitbook.com, there is an option to "synchronize with Git" using either GitHub or GitLab. As I don't use GitBook much anymore, I cannot investigate how this feature work, but I assume this is currently the 'recommended' approach - connect GitBook over to either GitHub or GitLab, and then git clone the repository from that site.

Original Answer, Last Edited on Jan. 27th 2018

Yes. You can clone the git repository where the GitBook resides on.

To clone the repository onto a local PC, type:

git clone https://git.gitbook.com/YOUR-USER-NAME/YOUR-BOOK-NAME.git

You will be prompted for your username for gitbook, and your password or an access token (i.e, an API Key). If you do not have a password, you may look up your unique access token in Settings -> Applications/Tokens.

You may also clone your git repository onto GitHub, but when you do so, GitHub will also ask for GitBook's username and password/access token so that it can read from Gitbook's git repository and just copy everything over. So you still need to have your username and your password/access token handy.

EDIT: When this answer was first written in January 2016, there was no official link to the git repository, making this an undocumented feature. Since then, the Gitbook team has exposed the URL to the git repository via its UI, as can be seen in this picture.