Slice the chicken breasts horizontally to create thin filets. Dip the chicken into a plate of flour, and shake off the excess.
Melt butter in the cast iron skillet over medium-high heat.
Add the breasts to the skillet and cook until browned and nearly cooked through. Remove the chicken from the skillet and set aside.
Add the garlic and shallots into the skillet and saute until the shallots are tender.
Add the mushrooms and continue to cook until they release their liquid. Carefully add the wine, and cook for two minutes.
Add the stock and simmer until the liquid begins to reduce.
Put the chicken breasts into the skillet with artichokes and cook until heated.
Season with salt and pepper to taste.
To serve, arrange the chicken on a serving platter and spoon the sauce over the top.