How to Make It
Bring 1 1/3 cups water and bulgur to a boil in a small saucepan over high. Reduce heat to medium-low; cover and simmer 10 minutes. Drain and rinse under cold water. Drain well; let dry on paper towels.
Meanwhile, heat a grill pan coated with cooking spray over high. Sprinkle chicken with 1/2 teaspoon salt and pepper. Grill chicken, turning occasionally, until done, 6 to 7 minutes. Remove to a cutting board. Let stand 3 minutes. Slice against the grain into strips.
Place bulgur, arugula, tomatoes, and peaches in a large bowl. Add remaining 1/2 teaspoon salt, oil, and vinegar; toss to coat. Divide mixture among 4 plates; top evenly with chicken.