Combine cream cheese and 1/2 cup sugar; beat until smooth.
Add egg, 1/8 tea spoon salt, and chocolate morsels, stirring well.
Combine flour, remaining 1 cup sugar, soda, 1/2 teaspoon salt, and cocoa; stir until blended.
Add water, oil, vinegar, and vanilla; stir until batter is smooth.
Spoon batter into paper-lined muffin pans, filling half full.
Spoon a tablespoonful of cream cheese mixture into center of each cupcake.
Bake at 350° for 25 to 30 minutes or until done.
Remove from pan; cool.