Preheat your grill to medium heat and brush the grill grate with oil.
In a small bowl, stir together the mustard, honey, and parsley; set sauce aside.
Place chicken between two pieces of waxed paper or plastic wrap and flatten each with the flat side of a meat mallet to an even thickness of about ½ʺ. Season with salt and pepper.
Set the flattened chicken pieces on the grill grate and cook about 3 minutes. Flip chicken and brush generously with the set-aside mustard sauce. Grill 2 to 3 minutes more or until golden brown and juices just run clear.
Transfer chicken to a platter and cover loosely with foil; let stand about 5 minutes.