Thaw shrimp as per package instructions and dry well.
In the bowl of a food processor, add half of the cooked shrimp, cream cheese, prepared horseradish, and cocktail sauce. Puree until completely smooth, taste and adjust seasoning with salt and freshly ground pepper. Add the remaining shrimp and pulse until chopped. Transfer dip into a serving bowl and garnish with chopped chives. Serve with butter crackers.
Tip: This dip is also great in a sandwich spread on a tea sandwich!