Heat oil in a large skillet over medium heat. Cut onion into small slivers and chop the garlic. Add the onion and garlic to a skillet and saute for 3 minutes. Season the chicken with salt and pepper and add to the skillet.
Saute until golden brown for about 2-3 minutes per side. Transfer the meat to a plate. Add the balsamic vinegar and ground ginger to the skillet and stir until the liquid is reduced by half.
Stir in the honey and then add in the fresh peaches and tomatoes. Add salt and pepper to taste. Return the chicken to the skillet, placing it in the middle between the peaches and tomatoes.
Allow the meat and sauce to simmer until it is cooked all the way through, about 12-15 minutes. Cover the skillet with a lid and reduce the heat to medium-low. Top with fresh basil.