Read Chrome browsing history within extension
Solution 1:
Retrieving the users history from javascript launched from a web page is impossible due to obvious blatant security issues.
Retrieving the users history from javascript running in an extension is possible, but doing so requires elevated permissions that the user has to grant after being warned. In summary you are probably looking for the chrome.history.getVisits() function. You can find more information on how to access the history using chrome.history here and the resulting security warnings given to the user here.