By the way, Microsoft seems to like to write this as "single page applications," but the lack of a hyphen in a compound adjective offends my Strunk and White-inspired grammatical sense. So I'll write it as "single-page applications" except where I'm referencing something that's specific to Microsoft.
ASP.NET's support for SPAs comes with the ASP.NET and Web Tools 2012.2 Update. The update contains a lot of great new tooling and template support for Visual Studio 2012 and will eventually become part of the next Visual Studio 2012 update.
The update now lets you create a Single Page Application template for an ASP.NET MVC 4 Web Application project, see Figure 1. At long last, we're finally filling up some of the blank space in this dialog box with lots of templates! This template is a good starting place that contains sample code for building a Todo list application that contains a single view. This template provides a solid foundation with all the tools you need for simple SPA applications.
Figure 1: Visual Studio 2012's New ASP.NET MVC 4 Project template dialog box that includes new Single Page Application template and four community-created templates installed.
Like ASP.NET MVC back in its youth, it will take some time to learn and feel comfortable with the MVC way of working with SPAs. I'm finding SPAs over traditional MVC to be as compelling of an evolution as MVC over Web forms were oh so long ago. Similar to my past experiences, I might never look back. I'm not going to rush out and rebuild any MVC or Web Forms apps using an SPA until they need a refresh, but I'll definitely be evaluating SPAs as the enabling technology for new applications. It's the next big thing, but it feels like a keeper.