In C#, do you need to call the base constructor?

You do not need to explicitly call the base constructor, it will be implicitly called.

Extend your example a little and create a Console Application and you can verify this behaviour for yourself:

using System;

namespace ConsoleApplication1
{
    class Program
    {
        static void Main(string[] args)
        {
            MyClass foo = new MyClass();

            Console.ReadLine();
        }
    }

    class BaseClass
    {
        public BaseClass()
        {
            Console.WriteLine("BaseClass constructor called.");
        }
    }

    class MyClass : BaseClass
    {
        public MyClass()
        {
            Console.WriteLine("MyClass constructor called.");
        }
    }
}