Perhaps I don't understand this fully, but I don't see how this works out to be competition from a "dollars and cents" perspective. Google keeps talking about Chrome being a way to "improve the web," and I see them doing that by promoting a browser that's leaps and bounds above the status quo (being IE). Having an officially "Google" product, instead of just a Google-sponsored one like Firefox, allows them to leverage their reputation in a way that hopefully gets people using modern browsers. There are good technical reasons to use both, and aren't crowding the market.
Until Google starts tightly coupling their web services with Chrome-exclusive features (and I don't mean just bookmark sync), Firefox and Chrome will both benefit Google economically by giving them a broader base of browsers capable of running their monetized products - rich web applications.
Firefox will not be an economic competitor to Google until (1) Firefox changes its search defaults or (2) Google elects to make Chrome-exclusive products or features.