Heat the vegetable oil in a large sauce-pan over medium-low heat. Add the diced leek; cover and cook for 10 minutes or until soft. Stir in the diced potato and chicken broth, and bring to a boil. Cover the potato mixture, reduce heat, and simmer for 15 minutes or until the potato is tender. Place the potato mixture in a blender or food processor, and process until smooth. Place the potato mixture in a large bowl, and cool to room temperature. Stir in the half-and-half, salt, and black pepper. Cover and chill. Sprinkle soup with minced chives.