There is now official implementation in the form of typescript-tslint-plugin. Please start using that, since this extension will no longer be maintained for Visual Studio 2017.
What is it?
Visual Studio 2017 extension for linting Typescript files using tslint. For Visual Studio 2015 version, go here.
How does it work?
When .ts is opened or saved, locally installed tslint is run in the background and code in the editor is underlined (marked) based on the tslint findings. Hovering over the underline gives additional info in the form of a tooltip and warnings and errors are listed in the Error List.
More information about tslint used by this extension.