Preheat the oven to 160C/325F/Gas 3. Lightly grease a 20cm/8in loose-bottomed cake tin or spring release tin.
Mix together the ingredients for the base and press into the prepared tin.
For the cheesecake filling, melt the chocolate in a bowl over a pan of hot water. Cool slightly.
Measure the cheese into a large bowl and beat until soft. Add the sugar and beat again until well mixed. Beat in the vanilla essence and then the eggs, one at a time. Spoon half the cheese mixture on to the biscuit crust, separating the spoonfuls. Add the melted chocolate to the remaining cheesecake mixture and stir well to mix. Spoon this mixture in between the cheesecake mixture already in the tin. Swirl the top to give a marbled effect.
Bake the cheesecake in the preheated oven for about 30 minutes or until the cheesecake becomes puffy around the edges but it still very soft in the centre. Turn off the oven but leave the cheesecake in the oven to cool.
Chill well and then loosen the cheesecake from the sides of the tin using a small palette knife. Serve well chilled.