Is it possible in .Net to catch all unhandled exceptions from any method in a class before its passed up the call stack?

Problem:

I would like to catch any exceptions from any method in a class so that I may record class specific data to the exception for logging before it is passed up the stack. I know that I can put a try-catch in every method of the class, but there are many methods and It seems there should be a more efficient way.

Example of what I am currently doing:

public class ClassA
{
    private int x;
    private int y;

    public void Method1()
    {
        try
        {
           //Some code
        }
        catch(Exception ex)
        {
            ex.Data.Add("x", x);
            ex.Data.Add("y", y);
            throw;
        }
    }

    public void Method2()
    {
        try
        {
            //Some code
        }
        catch (Exception ex)
        {
            ex.Data.Add("x", x);
            ex.Data.Add("y", y);
            throw;
        }
    }
}

Example of what I would like to do:

public class ClassB : IUnhandledErrorHandler
{
    private int x;
    private int y;

    public void Method1()
    {
        //Some code
    }

    public void Method2()
    {
        //Some code
    }

    void IUnhandledErrorHandler.OnError(Exception ex)
    {
        ex.Data.Add("x", x);
        ex.Data.Add("y", y);
        throw;
    }
}

public interface IUnhandledErrorHandler
{
    void OnError(Exception ex);
}

Note: This class is a service in a WCF project and implements a ServiceContract. I have tried adding an ErrorHandler to the service's ChannelDispatcher. However, when the error reaches the ErrorHandler it is already beyond the scope of the class where the error occurred, so I cannot access the class details.

Solution:

public class ClassC
{
    public ClassC()
    {
        AppDomain.CurrentDomain.FirstChanceException += OnError;
    }

    private int x;
    pri