It is open-source http://singularity.codeplex.com/ But is not properly FOSS. Currently it's available with the Microsoft Research License Agreement. So if you're interested / involved in any managed OS research, I wouldn't recommend looking at it. However, you might be interested in the bootable images.
I would call it "toxic-source" instead of "open-source".
If they ever decide to sue you for patent infringement over your singularity-like kernel, the fact you had access to their source code could be used to imply you infringed on purpose.
I advise anyone who is involved in any open-source project to stay as far away as possible from any Microsoft-originated code and to warn other developers of these risks.
There are many schools that have embraced the study of Microsoft code that are generating a steady flow of "land mines" who could end up employed in FOSS projects and who could conceivably be used as weapons in IP lawsuits.
Call me paranoid, but being paranoid doesn't automatically make me wrong. ;-)