1. Preheat the oven to 425°F. Coat an 11" x 9" baking pan and a rimmed baking sheet with olive oil cooking spray.
2. Place the carrots in the prepared baking pan. Sprinkle with the sugar, 1 teaspoon of the olive oil, and 1/8 teaspoon each of the salt and pepper. Toss to coat well. Roast, stirring several times, for 25 minutes, until the carrots are tender and lightly golden at the edges.
3. About 5 minutes before the carrots are done, place the chicken in a mound on the prepared baking sheet. Drizzle with 1 teaspoon of the oil, and sprinkle with 2 tablespoons of the chives, and 1/8 teaspoon each of the salt and pepper. Toss to mix. Arrange in a single layer. Roast, turning once, for 5 to 7 minutes, until cooked through. Remove carrots and chicken from the oven and let cool a few minutes.
4. Meanwhile, in a salad bowl, mix the vinegar, shallot, and the remaining oil, 2 tablespoons chives, and 1/4 teaspoon each salt and pepper. Let stand 5 minutes or more to blend the flavors.
5. To finish the salad, add the arugula, watercress, and grapes to the dressing and toss to mix well. Spread out on a platter. Top with the carrots, the chicken and any juices, and sprinkle with the pistachios. Serve warm.