Start by making the balsamic reduction sauce . In a small saucepan, heat the balsamic vinegar over medium-high heat. When it starts to boil, reduce it to low. Simmer, stirring often, until vinegar reduces and is thickened (about 15 minutes). Set aside.
Cut the chicken breasts in half and place on a cutting board and cover with plastic wrap. Pound the chicken breasts until about 1/2" thick.
Heat olive oil over medium-high heat. Meanwhile, salt & pepper the chicken.
Add the chicken to the pan and heat for 3-4 minutes, until browned. Flip and repeat on the other side. Remove to a cutting board and let rest for 5 minutes. Slice for serving.
Divide arugula between 4 plates. Top with chicken slices, peaches, tomatoes, mozzarella, basil and drizzle with the balsamic reduction sauce.
*grill the peaches for an even sweeter, deeper flavor