It handles Flash just fine, but no Java JRE (this is a conscious choice since it would be entirely capable with Chrome's Linux underpinnings). Client-side Java is quickly fading away so I assume that's why Google didn't bother. Naturally, Chrome OS doesn't support Sliverlight since it's a Microsoft technology, but Google has partnered with the world's most popular Silverlight app -- Netflix -- to create an HTML5 version of the Netflix Web player that will work in Chrome OS.
Anyway, it's a good point but Chrome does support the most popular of the three and will ultimately benefit from a world that's moving to HTML5 in the long run. With Chrome OS, I get the impression that Google sees this as a long game, and not one of its cute little experiments.
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