Assigning a value to an inherited readonly field?

The reason is that you can only assign to readonly fields in the constructor of that class.
According to the definition of readonly in the C# Reference (emphasis mine):

When a field declaration includes a readonly modifier, assignments to the fields introduced by the declaration can only occur as part of the declaration or in a constructor in the same class.

To work around this, you could make a protected constructor in the base that takes a parameter for the readonly property.

An example:

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

namespace ConsoleApplication1
{
    class Program
    {
        static void Main(string[] args)
        {
            Base b = new Child();
            Console.WriteLine(b.i);
            Console.Read();
        }
    }

    class Base
    {
        public readonly int i;

        public Base()
        {
            i = 42;
        }

        protected Base(int newI)
        {
            i = newI;
        }
    }

    class Child : Base
    {
        public Child()
            : base(43)
        {}
    }
}