Heat the oil in a saucepan over medium heat. Add onion, sugar, and garlic; sauté 5 minutes. Add tomatoes, 1 tablespoon chives, salt, pepper, and broth; cover, reduce heat to low, and simmer 20 minutes.
Place tomato mixture and yogurt in a food processor, and process until smooth. Pour mixture into a bowl; stir in milk. Cover and chill.
Ladle into individual bowls, and top with remaining chives.