In a large sauce pan heat the olive oil. Season chicken with salt and pepper, both sides then add it to the pan and cook turning once, until browned. Remove chicken to plate.
If there is a lot of extra fat in the pan remove all except approx. 1 tbsp. and then add your vinegar to pan. Do not put your head over the pan at this point or you will end up with a vinegar facial! Cook vinegar for a minute or two, scraping up any bits on bottom of pan then add approximately 1/4 chicken stock (a little more never hurt), maple syrup and a good amount of black pepper (to your taste of course). Cook until this mixture thickens a little. Then add your chicken & walnuts into the pan, spooning the sauce over of the chicken. Cover pan and simmer about 5-10 minutes.
Serve with noodles, roasted spuds or fluffy rice.
Tip: To toast your walnuts, preheat oven to 350. Place walnuts on parchment or foil lined baking sheet. Bake for approximately 5-8 minutes. Remove from oven and set aside.