Shake oil, vinegar, shallot, garlic, mustard, salt and pepper in a jar with a tight lid until combined. Set aside at room temperature.
Wash parsley leaves and spin dry. (Salad may be prepared to this point up to 6 hours ahead. Wrap parsley in damp paper towels and refrigerate in resealable plastic bags.)
To serve, toss parsley and chives with dressing in large bowl until well coated.