In a small bowl, combine mustard, oil, vinegar, hot pepper sauce, tarragon,, and pepper; mix well. Pour mixture into a large resealable plastic storage bag and add chicken breasts; close bag and knead until evenly coated. Marinate in refrigerator 1 to 2 hours.
Preheat grill to medium-high heat.
Remove chicken from marinade, discarding excess marinade. Grill chicken 10 to 12 minutes, or until no pink remains, turning it over halfway through grilling.
NOTE: While you're already firing up the grill, how about throwing on some baked potatoes?