Line a 3-cup capacity bowl w/ plastic wrap. In bowl, w/ mixer on medium beat cream cheese and horseradish sauce until smooth.
Stir in swiss cheese, celery, 1/4 cup parsley, onion & paprika. Spread mixture into bowl.
Cover, refrigerate at least 3 hrs. Invert bowl onto serving platter, remove plastic wrap. Mix chives and remaining parsley in small bowl. Press mix onto dip to cover. Serve w/ crackers and fresh cut veggies.