This post is influenced by this discussion on Meta Stack.

In Chrome, go to Settings -> Manage Search Engine. There add a new search engine:
Call it StackOverflow.com, give it keyword so and put this as a search url:  https://www.google.co.uk/search?q=site:stackoverflow.com+ %s.

Then add this as a default, but still make google your default engine. When opening new tab, in url type so, hit <tab>, and he-ho! enjoy!