Are you looking for WPF or WinForms? DevExpress and Infragistics both have tabbed MDI controls for WinForms. They seem designed to replicate the Visual Studio tabs, but you should be able to customise them to match Chrome.
Edit: as an open-source starting point you could try the one by Weifen Luo. It doesn't seem as customisable as the commercial ones, although I believe it supports rearrangement by dragging.
