1. Cut the green leaves and the root caps from the leeks; reserving only the section below the leaves. Cut the leeks in half lengthwise, and slice the halves into thin half moons. Soak sliced leeks in a bowl of water to clean. Drain.
2. In a large sauce pan, over medium heat, melt the butter and sauté leeks and green onions in the butter until tender for 15 to 20 minutes.
3. Add the chicken stock, diced potatoes, and thyme. Simmer until potatoes are just done, about 10 minutes.
4. Let it cool and puree in either a blender or food processor. Return to pot and add 1/2 cup sour cream. Stir until smooth and season to taste.
5. Chill the soup in the refrigerator for at least 2 hours before serving. Divide into 8 servings and top with a dollop of sour cream.