Season the chicken generously with salt and pepper.
In a heavy large frying pan over medium-high heat, warm the oil. Add the chicken and cook until brown, about 4-6 minutes on each side. Transfer the chicken to a plate.
Add the onion to the frying pan and stir. Add the potatoes and carrots. Sprinkle with salt and pepper and saute until the vegetables are beginning to brown, about 5 minutes.
Add the flour and stir to coat. Add the white wine, simmer until the wine has cooked off. Add the chicken stock and smoked paprika. Return the chicken to the pan and bring to a boil.
Cover the pan, place in the oven and bake for 40 minutes, or until the chicken and vegetables are cooked through.
Mix in the thyme. Taste and adjust the seasoning. Sprinkle with chopped parsley, then serve.
Little Helpers: If your kids are old enough to safely handle a vegetable peeler they can peel the carrots. I have a dull peeler that I let my 4 year olds use with supervision.Make Ahead: The carrots and onion can be prepped a day in advance.