From the days of the Microsoft antitrust trial in the 1990s, the company became known for the "embrace, extend, and extinguish" strategy it tended to employ when approaching any standard that had not been invented in-house. (The phrase came from internal Microsoft emails of the time.) So the industry has been understandably wary of the company's motives whenever Microsoft announced it was embracing some standard -- particularly if it was offering to extend it as well.
i-Programmer.info speculates that Hejlsberg took on this project because "a shift of power within Microsoft has made C#, and the whole .NET system, look less attractive... the re-imagining of Windows [with Windows 8] brought the limelight back on C++."
This early preview of TypeScript is integrated into Visual Studio 2012, and Microsoft has created what look like fairly rudimentary integrations for the Sublime, Emacs, and Vim editors. (Commenters on this Microsoft page urge the company to push the integrations in all three editors' native package-control environments.) There is an npm package for installing the compiler on a server running Node.js.
You can learn more about TypeScript and play with and download sample code on the language's public page. The code behind TypeScript is available as open source under the Apache 2.0 license (the TypeScript compiler is itself written in TypeScript). Microsoft hosts it on their own CodePlex repository, but commendably offers instructions for cloning it in git. The language specification itself is available under an Open Web Foundation's Final Specification Agreement license.