Preheat the oven to 325°F (160°C). Prepare a 9-inch springform pan by greasing the bottom and sides lightly.

In a medium-sized bowl, mix the graham cracker crumbs, melted butter, and sugar until combined. Press the mixture firmly into the bottom of the prepared pan. Bake for 8-10 minutes, or until lightly browned. Remove from the oven and set aside to cool.

In a large mixing bowl, beat the softened cream cheese with sugar until smooth using an electric mixer. Add the eggs, one at a time, mixing on low speed after each addition until just combined. Then, stir in the vanilla extract and sour cream until smooth and fluffy.

Take about 1 cup of the cheesecake batter and mix it with the melted chocolate until it’s well combined.

Pour half of the plain cheesecake batter into the prepared crust. Drop spoonfuls of the chocolate mixture on top. Continue layering with the remaining plain and chocolate batters, swirling them together gently with a knife for a marbled effect.

Bake in the preheated oven for 50-60 minutes, or until the cheesecake is set around the edges but slightly jiggly in the center. Turn off the oven and leave the cheesecake inside with the oven door slightly open for 1 hour to cool.

After cooling, refrigerate the cheesecake for at least 4 hours, preferably overnight, before serving to allow the flavors to meld perfectly.