In a small saucepan melt apple jelly over low heat. Remove from heat; stir in mustard. Reserve all but 2 tablespoons jelly mixture. Rinse chicken; pat dry. Grill chicken on the lightly greased rack of an uncovered grill directly over medium heat for 12 to 15 minutes or until an instant read thermometer inserted near the center registers 170 degree F, turning once and brushing occasionally with the 2 tablespoons jelly mixture during the last 5 minutes of grilling. Transfer chicken to a cutting board; cool slightly and bias-slice.
Meanwhile, toss the mesclun with the apples and walnuts. For dressing, stir together the reserved jelly mixture, vinegar, and oil. Divide the greens mixture among 4 dinner plates. Arrange chicken atop the greens; drizzle with the dressing. Makes 4 servings.