I'm unable to reproduce this behavior in .NET 4.0. Which version of .NET are you using ?
The only scenario I can think of that would produce the error message you report is if you tried to define MyVar the way it is now (non-static) inside another class which is static.
If that's the case then simply change 'MyVar's declaration to:
public static readonly string _objectString = ExtNameSpace.StaticClass.MyVar;
If that's not an answer, please show a selection of your code at the place where the variable _objectString is defined, and the declaration for the class it occurs in.