Using a large oven-safe cast-iron skillet over medium-high heat, then add oil. Once hot and shimmering, add the chicken and brown, skin side down for a few minutes. Add the shallots as well and stir them around to start caramelizing. Flip and sear the chicken on the other side for a few minutes.
4 Shallots
Flip the chicken back to skin side up. Pour the sauce over the chicken breasts in the skillet. Place in the oven for 20-25 minutes.
Remove from the oven and place 4-5 sliced peaches on top of each chicken breast, and nestle the remaining peaches into the pan around the chicken.
3-4 Small Peaches
Transfer the skillet to the oven and roast another 20-25 minutes or until the meat has an internal temperature of 165 degrees.
Notes
The recipe I was originally given, though it used a whole bird, appears to have been adapted from this recipe, http://iamhomesteader.com/roasted-peach-chicken/