Heat the oven to 350 degrees F. In a bowl, mash together the feta, rosemary, butter, and pepper with a fork.

Using your fingers and a spoon, push the feta stuffing under the skin of all the chicken parts except the wing; be gentle so as not to rip the skin. Put some stuffing under the tenderloin part of the breast. Season the parts well with salt and pepper.

Heat a deep, ovenproof, 10-inch skillet on medium heat until the pan is hot, at least 2 minutes. Add the olive oil and sear the chicken pieces, skin side down, until the skin is golden brown, about 4 minutes per piece; do this in batches if necessary. Transfer the chicken to a plate, drain the fat from the pan, and deglaze the skillet with the wine and broth or water, scraping up any stuck-on bits to dissolve them.

Return the seared chicken (skin side up) to the skillet, add the olives, and put the skillet in the oven. Bake until the juices run clear when pricked with a fork, about 40 minutes. Transfer the chicken and olives to a warm plate. Boil the juices in the pan over high heat until they reduce and thicken enough to coat the back of a spoon, about 4 minutes. Pour the sauce over the chicken pieces and serve.