Heat a large cast iron skillet over medium heat. Add oil to the pan and coat. Sprinkle salt and pepper over the chicken to season. Add the chicken to the pan, and begin to cook until slightly browned, for about 4 minutes per side.
Move the chicken to the outer edges of the skillet, and place the butter in the center. When the butter has melted, stir the garlic and rosemary into the butter, and let cook for about 1 minute, stirring.
Add the cream and salt and pepper. Increase the heat to high, and simmer the cream until thick enough to coat the chicken, about 2 or 3 minutes, turning the chicken in the sauce as it reduces.Serve the chicken hot, topped with the remaining sauce. Enjoy Chicken With Rosemary Garlic Cream!