Actually, Google don't care which browser you use. This isn't an attempt to take over from firefox.
Instead, it's an attempt to start a trend towards faster and more stable web browsers - so that people will be more willing to move to cloud computing platforms. That's where google's real interests lie.
If you're using firefox or IE but also using Gmail, Google Reader, Blogger, Google Chat, Google Alerts, Orkut, Google Analytics, Google Docs, Google Base and Google Picasa then you're already on the majority of their cloud computing platform. They don't need to convince you that it's the way to go.
but.
If you don't use those things because your browser is slow or crashes, then they're hoping that chrome (when it's finished and released - remember it's very early beta) will convince you that it's viable.