Preheat your oven to 375°F.
In a Dutch oven, heat olive oil and butter over medium-high heat.
Season chicken thighs with salt and pepper and add them to the Dutch oven skin-side down. Brown them for about 5-6 minutes until golden brown. Then turn them over and brown the other side for an additional 3-4 minutes.
Remove the chicken thighs and set them aside. Add onion, garlic, carrots, and celery to the Dutch oven and sauté for about 5-6 minutes until softened.
Pour in chicken broth and white wine and stir to scrape the browned bits from the bottom of the pan.
Stir in Dijon mustard and thyme leaves.
Return the chicken thighs to the Dutch oven, skin-side up. Cover the Dutch oven with a lid and bake in the oven for about 40-45 minutes until the chicken thighs are cooked through.