Wash peaches, rubbing to remove fuzz. Cut in half; remove pits. Thinly slice peaches. Place peach slices in large bowl. Add 1/2 tablespoon lemon juice; toss. Whisk 1 1/2 tablespoons lemon juice and olive oil in small bowl. Whisk in cream, then chives. Season with salt and pepper. Add arugula to bowl with peaches. Add dressing and toss. Season with more salt and pepper, if desired, and serve.