If you've formatted the PC and the only place you had stored the bookmarks was locally, then no. Since you've formatted it, so the data's gone, barring attempting data retrieval with no assurance of success.
However, Chrome automatically stores your bookmarks and similar in the Cloud if you logged into your Google account with the appropriate settings enabled. In the Chrome Settings page, choose to sign in to Chrome with a Google account, which will, provided you had synchronised them previously, download all your bookmarks for you automatically.