Heat skillet over medium-high heat. Lightly coat chicken breasts with olive oil. Sprinkle with salt and pepper. Add chicken to pan when hot. Cook 4-5 minutes per side or until cooked through. Remove from heat and keep warm.
Meanwhile, melt butter in a saucepan over medium heat. Add flour and whisk constantly for one minute. Gradually add milk, whisking constantly. Stir in chives and reduce heat to medium-low. Simmer 5-7 minutes or until thick, stirring occasionally. Add cheese by the handful and stir until cheese is melted.
Spoon sauce over chicken and garnish with additional fresh chives, if desired.
You may have extra sauce, depending on how saucy you like your chicken.Recipe adapted from Cooking Light Magazine.