Heat oil in a large skillet over medium heat. Saute chicken until lightly browned; set aside. Melt butter in skillet, and saute garlic for 1 minute. Stir in flour, and cook for 1 minute. Remove from heat. Mix together cream and milk, then gradually whisk into flour mixture until smooth. Whisk in mustard. Return pan to medium heat, and stir constantly until mixture boils and thickens. Stir in chicken, Parmesan and chives. Cook, stirring, until heated through.