OK this worked for me.
- Open the solution in Visual Studio 2013
- Select File | Add to Source Control
- Select the Microsoft Git Provider
That creates a local GIT repository
- Surf to GitHub
- Create a new repository DO NOT SELECT Initialize this repository with a README
That creates an empty repository with no Master branch
- Once created open the repository and copy the URL (it's on the right of the screen in the current version)
- Go back to Visual Studio
- Make sure you have the Microsoft Git Provider selected under Tools/Options/Source Control/Plug-in Selection
- Open Team Explorer
- Select Home | Unsynced Commits
- Enter the GitHub URL into the yellow box (use HTTPS URL, not the default shown SSH one)
- Click Publish
- Select Home | Changes
- Add a Commit comment
- Select Commit and Push from the drop down
Your solution is now in GitHub