Preheat oven to 350°F.
Pat the chicken dry with paper towels, and season with salt and pepper to taste.
Heat the oil in a large oven-proof skillet over medium-high heat until shimmering.
Add the chicken and cook until browned, about 2 minutes per side.
Remove to a plate and set aside.
Decrease the heat.
Add the shallot and cook until translucent, about 3 minutes.
Add the ginger and garlic to the pan and cook until fragrant stirring constantly, 45 to 60 seconds.
Add the chopped basil, chicken stock and peaches.
Return the chicken to the pan and turn to coat.
Transfer to the oven and bake until the juices run clear when the chicken is pierced with a knife, about 15 minutes.
Slice the chicken and serve immediately.