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.