It's called the search box, and you can change your default search engine. Even though I submit patches to Firefox, Chrome is the better browser until some serious overhauls are made in Firefox.
EDIT: My opinion on Firefox: it's slow and tends to crash more often, the browser itself is a huge system resource hog, and the Gecko layout engine needs some serious performance overhauls, and it needs to use a better Javascript engine (like Google's V8, or even Apple's JavaScriptCore engine even though it doesn't fully support ECMAScript 5); however, Firefox has some amazing built-in developer tools, is at the bleeding edge of standards compliance and emerging web technologies, and is the only project that truly competes with and has potential to knock out Chrome and Safari (because of the developer base). Chrome is great since it's fast (only because it caches everything), runs each tab in its own system process (great if a page freezes since you can just kill the process containing the tab instead of killing the entire browser), and you just can't beat any work being done by Google in the web arena right now. Chrome boasts one of the fastest layout engines (a highly optimized WebKit engine), one of or the fastest Javascript engines available, support for absolutely incredible media codecs, fastest support and inclusion of the absolute newest web standards, and an incredibly secure and stable browser. However, since each tab runs in its own process you can see Chrome eating up CPU cycles if you have multiple tabs doing "intensive" work, the cache system which speeds up browsing can mean that malicious code from websites stays on your computer for longer (which is true of any browser, but Chrome caches everything), and the developer tools just aren't the same quality (my opinion) of the Firefox developer tools. Both browsers are great and I use both on a regular basis, but my default is Chrome simply because of its speed and security.