Preheat your grill pan (or grill) over medium heat until it is searing hot.
While your pan preheats, chop your rosemary and combine with salt and pepper in a little bowl. Rinse and pat your chicken breasts dry and rub the rosemary mix on both sides. Set aside until your pan is finished heating.
When it is searing hot, brush olive oil over the grates with a heat proof grill brush.
Immediately place both chicken breasts in the grill pan towards the center but not touching. Place a 10” cast iron skillet on top of the chicken. You should cover the bottom of your skillet with aluminum foil for easy cleanup and zero cross contamination. Cook on first side for 5 minutes.
Remove skillet and swap out the foil, flip chicken and place skillet back on top of the chicken. Cook for an additional 4-6 minutes. For medium sized breasts I usually cook it a total of 8 minutes. Be sure to test with an instant read thermometer or, if you cook chicken frequently, you can probably press on it and know when it’s done.
Remove from skillet, tent loosely with foil, and let rest 10 minutes before cutting.