Update 10/31/2013: The WebViewChromium is now implemented in Android 4.4 KitKat!
To combat this problem, Google has promised “Chromium” implementation for the WebView – essentially using the Chrome rendering engine to power WebView. This was first talked about at Google IO 2012. Android 4.3 shipped yesterday, and WebViewFactory shows experimental support for Chromium. However, the crucial webviewchromium.jar is still missing from the /system/framework directory to enable this support.
So for now, we’re still left where we were. One can only hope for the next release to finally have this working out of the box.