Melt the butter in a large skillet over medium heat. Add the onion and cook 5 minutes. Add the sugar snap peas and cook, stirring occasionally, until bright green and crisp-tender, about 5 minutes. Mix in the sugar and salt and cook 1 minute more. Stir the half-and-half with 3 cups of water in a large measuring cup. Place half the snap-pea mixture in a blender or food processor. Pour in half the water mixture and puree until very smooth, 30 to 60 seconds. Repeat with the remaining ingredients. Pour the soup through a strainer and chill for at least 4 hours. Sprinkle with the chives (if desired) before serving.