Question: Why doesn't Chrome have a search box?
For a long time, Web browsers didn't have a search box. If you wanted to search, you went to your favorite search engine's website. To save time, Web browsers like Firefox, Safari, and IE included a separate search box right in the browser bar. Why is it that Google Chrome doesn't have one?
Answer: Chrome saves the search box space by combining the search box with the URL address box. The combined omnibox lets you type keywords or URLs into the same box, and Chrome interprets your intent.
Using the omnibox is a new habit, but it's an improvement over using two boxes or going to the Google home page every time you want to search.

