Whisk lemon juice, mustard, and sugar together in a bowl. Add chives and whisk in oil in a slow stream. Season dressing with salt and pepper.
Quarter each heart of romaine lengthwise. Trim core at ends. Place 2 quarters on each salad plate. They're served whole, covered with dressing. Halve a few grape tomatoes and place at plates' edge for garnish. Drizzle salads liberally with vinaigrette and serve.