In a high-sided skillet, cook garlic and leeks in butter and olive oil over medium heat until tender, approximately 4 to 5 minutes.
Add the potatoes and chicken broth. Bring to a rapid boil, then lower the temperature to just below medium. Cover the skillet loosely with a lid and simmer for 25 to 30 minutes, until the potatoes are tender.
While the potatoes are simmering, add the sour cream and heavy cream to a bowl. Season with salt and pepper to taste and set aside.
Remove the skillet from heat and let cool. In a heavy-duty blender, blend potatoes in batches until a smooth consistency is achieved, approximately 1 to 2 minutes.
Temper sour cream and heavy cream with 2 to 3 tablespoons of the purée. Add the tempered sour cream mixture to the rest of the purée and season with salt and pepper to taste.
Place the soup in an airtight container and refrigerate for 3 hours or overnight. Chill thoroughly and garnish with fresh chives to serve.