As several users have already said, you can't catch the exception. However, if you're struggling to find out where it's happening, you may want to configure visual studio to break when it's thrown.
To do that, you need to open Exception Settings from the 'Debug' menu. In older versions of Visual Studio, this is at 'Debug' - 'Exceptions'; in newer versions, it's at 'Debug' - 'Windows' - 'Exception Settings'.
Once you have the settings open, expand 'Common Language Runtime Exceptions', expand 'System', scroll down and check 'System.StackOverflowException'. Then you can look at the call stack and look for the repeating pattern of calls. That should give you an idea of where to look to fix the code that's causing the stack overflow.