In a nonstick 12-inch skillet, heat oil over medium heat. Sprinkle chicken with salt and 1/4 teaspoon pepper. Add chicken to skillet and cook 6-8 minutes or until chicken loses its pink color throughout, turning once through cooking. Transfer to a plate. In the same skillet over medium heat, with whisk, stir in flour and cook 30 seconds, stirring. Add half and half; heat to boiling. Add cheese and stir until melted. Remove skillet from heat and stir in pesto and remaining 1/8 teaspoon pepper. Serve chicken with pesto sauce.