Don't get greedy, Google (NASDAQ:GOOG).

It's been more than a year since the search-engine giant introduced its Web browser. Google Chrome is slick, quick, and highly praised.

On the downside for Google, Chrome commands a mere 2.8% slice of the browser market, according to marketing-research firm Net Applications. It trails Microsoft's (NASDAQ:MSFT) Internet Explorer (67%), Mozilla's Firefox (23%), and Apple's (NASDAQ:AAPL) Safari (4%).

There's nothing wrong with being a bit player in the battle of the browsers, but Big G has loftier goals.

"If at the two-year birthday we're not at least 5% (market share), I will be exceptionally disappointed," Chrome Engineering Director Linus Upson told Reuters this week. "And if at the three-year birthday we're not at 10%, I will be exceptionally disappointed." He conceded that Google's internal goals are even more ambitious than that.

The problem is that you can't take market share unless it's at someone else's expense. It would be easy to assume that Google will overtake Apple, but Safari has been gaining as a platform, given the success of Apple computing products (and the Safari-powered iPhone). It's also been trying to woo converts with every iTunes update.

Firefox has historically grown by nibbling at Microsoft's market share, but both companies are perpetually updating their platforms to make sure that no one else comes out with a superior product.

Firefox offers a customizable browser that positions itself as the anti-Microsoft. Meanwhile, Microsoft ensures that the latest version of Internet Explorer is loaded into every new Windows operating system.

In short, Google has a problem on its hands if it seriously thinks it can double its market share every year.

It may want to aim at Microsoft -- and it has -- but if it wants to be in Firefox's shoes as the IE antidote, it's going to have to gun for Firefox at some point.

Google doesn't always get what it wants. It has clobbered Microsoft and Yahoo! (NASDAQ:YHOO) in search, but it still trails the competition in nearly every other category where it has tried.

There's nothing wrong with aiming for the fences, but Google needs to know that it has three strong competitors ahead of it. And now that computing and smartphone devices are converging, it won't be long before even more well-backed players want some skin in authoring the browsing experience.

It would be great to see Google double its market share over the next year. Chrome is certainly worthy. However, just as Microsoft used to point to lofty -- and ultimately unattainable -- market-share goals in the search arena, Google had better get used to competing against rivals that won't go down quietly. 

Google is a Motley Fool Rule Breakers recommendation. Microsoft is a Motley Fool Inside Value pick. Apple is a Motley Fool Stock Advisor selection. Try any of our Foolish newsletter services free for 30 days.

Longtime Fool contributor Rick Munarriz isn't calling for a search-engine search party, but he may as well. He owns no shares in any of the stocks in this story and is also part of the Rule Breakers newsletter research team, seeking out tomorrow's ultimate growth stocks a day early. The Fool has a disclosure policy.