Heat a large, deep skillet over medium high heat. Season chicken with salt and pepper. Add 2 tablespoons extra-virgin olive oil, half the chicken pieces, and a couple of crushed cloves of garlic.
Brown chicken 2 minutes on each side and remove from pan. Add remaining oil, another single turn of the pan, remaining chicken pieces and garlic. Brown chicken 2 minutes on each side and remove. Add vinegar to the pan. Let it cook off.
Add butter, shallots, and rosemary to the pan and cook 2 minutes, add flour and cook 1 minute more. Whisk in wine, reduce 1 minute. Whisk in broth and bring liquids up to a bubble. Return chicken to the pan and simmer over moderate heat 7 to 8 minutes to finish cooking chicken through.
Dessert: This is a very rich meal. My suggestion for dessert is to set out a small cookie tray and offer coffee or tea.