There is no Chrome on Android 2.3 phones (still very common on old and low spec phones). The stock 2.3 browser gives me a blank screen when I run my Dart regression tests. I tried Opera on my 2.3 test phone and ran some regression tests and it looked better - didn't finish the tests, but there was at least something to see (actually, it looked like the same problem I see running my tests on IE10 at the moment, so I expect that will cleared up sooner or later).
Not suggesting you make Chrome for 2.3 - I know that's out, from what I've read. It may helpful, however, to work with a partner (Opera?) to ensure there is _something_ where Chrome is not supported. Something that will at least execute the javascript generated by dart2js.