Preheat the oven to 400F. In a stove-top and oven-safe Dutch oven or oven-safe skillet, heat the oil over medium high heat. Dry the chicken pieces well by patting them with a paper towel. Sprinkle the chicken pieces with a bit of salt and the pepper. Cook the chicken until well browned, turning regularly, for about 8 minutes, then remove chicken to a plate. You can remove and discard some of the fat in the pan if you have lots, but do leave a bit to cook the garlic in the next step.
Reduce the heat to medium, add the garlic, and cook, stirring regularly, until it is starting to brown, about 3 minutes. Sprinkle the flour over the garlic and stir until combined. Return the chicken to the pan, COVER, and bake for about 15 minutes in the pre-heated 400° oven (If you pan or skillet doesn't have a lid, you can tightly cover the top with tin-foil instead.) Be sure to cook until the chicken is cooked to 165F internal temperature. *Chicken breasts will take longer.
Remove the pan from the oven and put it on a burner. Be careful not to touch the hot pot! Remove the chicken pieces from the pan to a clean plate. Over medium-high heat, whisk in the wine and simmer for 1 minute to cook off the alcohol. Whisk in the broth, thyme and a bit more salt and pepper, then reduce heat and simmer, stirring regularly, until the gravy thickens. Turn the heat off and stir in the butter. Taste sauce and add more salt and pepper, if it needs it. Add the chicken back to the pot to re-warm with the sauce. Serve spooned over mashed potatoes, rice or pasta.
Be sure to read the Ingredient and Cook's Notes above the recipe card for more tips, options, substitutions and variations for this recipe!