This is speculation, but I guess that Chrome will likely support dart natively in the future. It will mean that Chrome will be able to outperform other browsers that don’t have the native support.
Update: There’s a hint from The Official Google Code Blog that it might be coming:
The Dart VM is not currently integrated in Chrome but we plan to explore this option.
Update 2: It looks like I was right! Here’s some recent news:
Additionally, and perhaps most importantly, Google is releasing Dartium, a Chromium build with native Dart support.
It’s more than likely that Dartium is part of a series of steps that Google will be taking to launch native support in Chrome — greatly improving the usefulness of Dart. Bringing native support into other browsers like Firefox and IE, on the other hand, will be quite the challenge.
Update 3: Since I posted this answer, Microsoft have released TypeScript which is a competing technology. I’d say it’s unlikely that Microsoft have any intention of integrating Dart into Internet Explorer as they would probably prefer people to use TypeScript rather than Dart.