Just to clarify, in Chrome this works automatically. After performing one search on Stack Overflow, you can now start typing "stack overflow" into the address bar. As soon as you see that the first autocompletion is StackOverflow.com, you can hit tab and perform a search.

This works automatically with any site you perform a search on, with no need to configure anything. One of the main reasons I moved to Chrome after years of being an FF user.