To be able to add a Child Publication, you must first create a Structure Group in the Parent Publication (normally an empty Structure Group). This is mentioned here: Tridion 2013 creating a BluePrint structureTridion 2013 creating a BluePrint structure
Alternatively, there are known issues with later versions of the Chrome browser. You may want to try this in another browser. If this fixes the problem, then you should install Hotfix Rollup 1 (HR1) for Tridion 2013 SP1.
If the problem persists, you could try raising this with Tridion Support