Heat oil in a heavy-bottomed oven-safe pan. When shimmering, add chicken, carrots, celery, onion, thyme, parsley, salt and pepper. Stir well and spread evenly in pan. Transfer pan to preheated 350°F oven for 30 minutes, stirring occasionally, until everything is golden brown.
Add white wine and chicken stock. Stir, scraping up and browned bit on the bottom of the pan. Simmer 5 minutes until liquid reduces about half.
Strain sauce, pressing down on vegetables with the back of a ladle. Discard solids. Add butter and swirl pan until it melts and sauce is thick and glossy. Adjust salt and pepper.