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BEAT egg lightly in medium saucepan with wire whisk. Add sugar and tapioca; mix well. Gradually add milk, beating well after each addition. Let stand 5 minutes. Add chocolate. Bring to boil on medium heat, stirring constantly. Reduce heat to medium-low; cook until chocolate is completely melted, stirring constantly. Remove from heat.
STIR in vanilla. Cool 20 minutes; stir. (Pudding thickens as it cools.)
SERVE warm or chilled. Store leftover pudding in refrigerator.