Google Chrome’s combined address and search bar is called the Omnibox.
The name reflects its two jobs: it accepts web addresses and also sends ordinary words to the user’s default search engine. Chrome’s interface helped popularize the idea of merging these controls instead of keeping a separate address field and search box.
The Omnibox also provides autocomplete suggestions. As someone types, Chrome may suggest previously visited pages, matching URLs, popular searches, or site-specific searches. Users can sometimes press Tab to search a particular website directly from the same field.
A common mix-up is “omnibar,” a term used informally and by some other browsers. “Awesome Bar” is associated with Firefox, while “Smart Bar” and “Search Box” are generic descriptions rather than Chrome’s canonical product name. The Omnibox is therefore the fair single answer for this question.