Google developed Chrome because making the web as a viable application platform is in their best interest. They tried working with Mozilla for Firefox 2 development, but realized that Mozilla is a dysfunctional project with questionable leadership and insular development practices, so working with them really wasn't tenable. Hence, Chrome.

And honestly, process-per-tab, a proper security model, and plugins running as a separate process so the buggy Flash plugin doesn't bring down your browser are things that Firefox is considering copying from Chrome, not the other way around.