Melt the chocolate in a small clean sauce pan. Melt the chocolate GENTLY over low heat, be sure not to burn it. Or you can use a microwave. Set aside to let cool.
In a large bowl using a hand mixer, beat the cream cheese, sugar, and vanilla together. Beat until the sugar is entirely incorporated and the mixture is creamy and light.
One at a time, add in the eggs. Make sure to blend each egg in fully before adding the next.
Remove two cups of this batter and place it in a clean, medium-sized bowl.
Add the melted chocolate to the two cups of batter in the medium-sized bowl. Beat together with a hand mixer until the chocolate is combined and homogeneously spread throughout.
Pour the plain batter on the baked crust.
Pour the chocolate batter in a random movement pattern over the plain batter.
With a knife or toothpick, swirl the batter to create a marbled effect. I like to go a little deep for my marbled cheesecake, but if you do this, be sure not to disturb the crust on the bottom.
Bake in the preheated 325°F oven for 40-50 minutes, or until the center is just set,. You want just a little wobble in the center still when you take it out.
Allow the cooked cheesecake to cool in the pan for 1-2 hours until it reaches room temperature. Then, cover the pan loosely with plastic wrap and allow it to refrigerate for at least 4 hours before serving.