Chrome faciliated faster web browsing, meaning more searches which translate into more ad revenue for Google. Then, the obvious motivation of developing an OS came up to increase the volume of Web activity itself. Google wants everyone to keep searching & searching fast.
The Chrome operating system is said to be released next year, but will it ever lure the mom and pop to move to this new browser? All said & done, Intel would definitely doesn't want this to happen - otherwise, with little of client processing - what is the use of the CPU horse-power?