Melt butter and whisk in mustard, apricot preserves, and red pepper. (Sauce may be prepared ahead of time and refrigerated. Warm slightly and whisk to a smooth consistency before serving.)
Grill or broil chicken until browned. (Parboil or microwave chicken to shorten cooking time, if desired.) Chicken is done when juices run clear and it is no longer pink inside.
Use about half the sauce to baste frequently during final cooking stage. Serve chicken hot accompanied by remaining sauce.