Combine peaches and fresh lemon juice in medium bowl. Place red bell pepper and onion in medium non-stick saucepan. Stir over medium-low heat until vegetables are crisp-tender, about 6 minutes. Add curry powder and cayenne pepper to saucepan and stir 1 minute. Add brown sugar and stir until dissolved, about 2 minutes. Add vinegar; stir 2 minutes. Add peach mixture and accumulated juices to pan and cook until heated through, about 3 minutes. Transfer to a bowl and cool completely. Season relish to taste with salt and pepper. (Can be prepared up to 5 days ahead. Cover and refrigerate.) Mix chopped cilantro into relish.

Prepare grill. Season chicken with salt and pepper. Grill until just cooked through, about 5 minutes per side. Cut chicken into thin diagonal slices. Arrange on plates; surround with peach relish.