Is it possible to implement an inheritance chain using only abstract classes?

Yes, in C# it is possible to implement an inheritance chain using only abstract classes. An abstract class can inherit from another abstract class, thus creating a chain.

For example:

public abstract class Animal {
    public abstract void MakeSound();
}

public abstract class Mammal : Animal {
    public abstract void Walk();
}

public class Dog : Mammal {
    public override void MakeSound() {
        Console.WriteLine("Bark");
    }

    public override void Walk() {
        Console.WriteLine("Dog is walking");
    }
}

Here, Mammal inherits from Animal, both are abstract, and Dog implements the concrete methods. Thus, an inheritance chain of abstract classes is quite possible.