In a sauté pan large enough to hold all the chicken pieces in a single layer, gently sauté the garlic, rosemary and (if using) the red pepper just until the garlic begins to brown around the edges. Remove.
Raise the heat to medium-high and add the chicken pieces to the pan. Brown them well on all sides, seasoning with salt and pepper as you go.
Add a splash of white wine and let it simmer for a minute or two.
Then lower the heat, add the giardiniera and olives, cover the pan and let the chicken braise turning from time to time, for about 30-45 minutes or until the chicken is cooked through and very tender.
Uncover the pan, turn up the heat to medium and cook off most but not quite all of the cooking juices.
Serve immediately.