Google has made Dart and its development tools open source in order to grow its developer base. As of now, there are no browsers, including Google's Chrome, that have native support for Dart. Since Dart is being developed solely by Google, they will need to convince the other browser vendors to support its new web programming language. They will also need to engage web application programmers to learn Dart and its associated development tools. Hence, the acceptance of Dart rests heavily on Google's handling of matters on these two fronts.
Source: Google Code blog