In a large skillet, add olive oil and heat over medium-high heat. Season chicken with salt and pepper and add to the hot skillet. Cook until both sides are golden. Remove from pan and set aside.
Turn skillet down to medium and add butter. Add in flour and whisk together. Then whisk in the lemon juice.
Slow whisk in chicken broth followed by the cream and rosemary. Bring to a gentle boil and add chicken back to the skillet. Cook for 5 minutes at a gentle boil. Then remove from heat and allow to sit for 5 minutes. Double check that chicken is fully cooked before serving. Serve over hot cooked pasta or rice. Serves 6.