2 large (about 1 lb) ripe but firm peaches, cut into 1/4 inch wedges
2 tbsp fresh shredded basil or chopped thyme
Remove the tenderloin (the finger size muscle on the underside of each chicken breast) and set aside. Using the flat end of a meat pounder, lightly flatten each chicken breast.
Season the chicken breast and tenderloin with salt and pepper; dredge with the flour, shaking off excess.
In a large skillet over medium-high heat, melt 1 Tbsp of the butter. Add the chicken and sauté until just cooked through, about 2 minutes per side. Chicken is done when instant-read thermometer inserted in thickest part of breast reads 165°F. Transfer the chicken to a plate and cover while you make the sauce.
Add the remaining 1 Tbsp butter to skillet. When the butter is hot, add the shallots and sauté until tender, about 30 seconds. Add the vinegar and cook until reduced by half, forming a thick glaze, about 2 minutes. Add the chicken broth and cream, along with any juices collected on the chicken plate. Cook until the sauce is reduced by half and lightly coats the back of a spoon, about 2 minutes. Add the peaches and toss until just warmed though. Do not overcook. Remove the sauce from heat and stir in the basil or thyme. Adjust seasoning with salt and pepper.
Place the chicken on warmed dinner plates or on a platter. Spoon the sauce and peaches over the chicken and serve immediately.