Yahoo used as an example.
The slow copy-paste way:
CTRL-L+A+X Yahoo.com (type till tab-complete appears) Keywords TAB CTRL-V ENTER
The fast short keywords way:
Right click on the address bar and click
Edit search engines...
Enter short keywords for the search engines. (e.g.
g for google,
b for bing,
y for yahoo)
CTRL-L HOME y Keywords SPACE ENTER
The extension way:
This extension embeds the options under the search and allows you to select your search term and click.
You still would have to do it manually for Stack Overflow though, it doesn't take that much effort...
There is no way to get the search term to natively stay as there is no search box in Google Chrome!