In a small bowl, whisk together the honey, mustard, thyme, and 1 tablespoon of the oil.
Heat grill to medium-low. Season the chicken with ¹/₄ teaspoon each salt and pepper. Grill, covered, turning occasionally, until cooked through, 25 to 30 minutes; brush frequently with the honey mixture during the last 5 minutes of cooking.
Meanwhile, in a medium bowl, whisk together the vinegar, the remaining 3 tablespoons of oil, and ¹/₄ teaspoon each salt and pepper. Add the arugula and plums and toss to combine. Serve with the chicken.