Remove casing from chorizo; crumble chorizo. In small skillet over medium-high heat, cook chorizo until well browned, stirring occasionally. Remove to plate.
Shred half of cheese to make 1 ½ cups. Cut remaining half into ½-inch cubes. In large bowl combine mashed potatoes, shredded cheese, chives, salt and pepper; mix well. Shape mixture into 2-inch balls. Press thumb into center of each ball to make an indentation. Add some crumbled cooked chorizo and cube of cheese into indentation. Pinch potato mixture around filling to enclose completely. Repeat with remaining mixture.
Roll each potato ball in flour to cover completely. Then roll in beaten egg; roll in breadcrumbs to coat completely. Repeat with remaining ingredients.
Heat oil 2 inches vegetable oil in medium saucepan. Or, heat oil in deep-fryer to 350°F. Fry potato balls, a few at a time, until golden brown and crisp, about 3 minutes. Repeat with remaining potato balls. Garnish with chives.