In a small bowl, beat egg yolks until thickened and lemon-colored.
Heat sugar and water in a small saucepan until mixture begins to boil.
Gradually pour hot mixture over egg yolks, beating constantly.
Heat chocolate chips and butter until chocolate melts. Stir in rum; set aside.
Place bowl with egg yolk mixture in a pan with almost boiling water. Beat egg yolk mixture five minutes or until doubled in volume.
Remove bowl from hot water and mix for five more minutes. Pour into a large bowl.
Fold (do NOT stir!) chocolate mixture into egg yolk mixture.
In a small bowl beat egg whites with cream of tartar until stiff but not dry.
Fold (do NOT stir!) beaten egg whites into chocolate mixture. Spoon into dessert dishes. Refrigerate several hours.