Sprinkle chicken with salt and pepper; dust with flour. Melt butter in heavy/large skillet over medium-high heat. Add chicken to skillet and sauté until brown (about 3 minutes per side). Using tongs, transfer chicken to plate.
Add prepared-halved baby artichokes, onion, mushrooms and Italian seasoning to skillet. Sauté until onion is tender (about 6 minutes). Add broth and wine and boil until liquid is reduced by half (about 8 minutes).
Return chicken and any accumulated juices to skillet. Cover and reduce heat to medium-low. Simmer until chicken is cooked through and artichoke hearts are tender (about 5 minutes). Season to taste with salt and pepper and serve.