The Sidebar API is a proposal/concept for adding a sidebar surface to allow chrome extensions an alternative to injecting iframes into pages in order to display something next to a page.

With it, you could implement something like the old Side Tabs feature (that you mention), which was removed from Chrome due to "the complexity of a tree-style interface in terms of usage is beyond what most users need or want, and in terms of implementation is more than passes the cost/benefit test for building into Chrome natively as an option."[1])

[1]: https://code.google.com/p/chromium/issues/detail?id=344870#c...