1. Preheat oven to 350°. Bake pecans in a single layer in a shallow pan 10 to 12 minutes or until toasted and fragrant, stirring halfway through.
2. Preheat grill to 350° to 400° (medium-high) heat. Gently toss peach halves in 1 Tbsp. olive oil; sprinkle with salt and pepper to taste. Grill peaches, cut sides down, covered with grill lid, 2 to 3 minutes or until golden. Turn peaches, and place 1 cheese piece in center of each peach; grill, covered with grill lid, 2 to 3 minutes or until cheese begins to melt.
3. Toss arugula with remaining 2 Tbsp. olive oil and salt and pepper to taste. Arrange arugula on a serving platter; sprinkle with toasted pecans, and top with grilled peach halves. Drizzle peaches with honey, and sprinkle with chives.
*Aged balsamic vinegar may be substituted.