Heat oil in a large skillet over medium high heat.
Sprinkle chicken on both side with salt and pepper, then place chicken and flour in a plastic bag and shake well to coat the chicken.
Place chicken in large skillet and brown on both sides, about 4 minutes each side. Remove chicken from pan and set aside.
Add chicken stock, peaches, brown sugar, vinegar, nutmeg, and minced garlic the skillet. Stir mixture, scraping up any browned bits; bring to boil and reduce heat to low.
Add chicken to the skillet. Simmer for 10 minutes, remove from skillet, and serve.