For crust, combine crumbs and butter in a small bowl; mix tell well combined. Press into a greased 9" springform pan, pressing up the sides.
Preheat oven to 325°.
For the filling: Beat cream cheese in a large bowl till smooth. Gradually beat in sugar, scraping sides of the bowl often. Slowly beat in the sweetened condensed milk, scraping the sides of the bowl often.
Add eggs, vanilla, and lime juice, beat on low speed just till blended.
Melt the 3/4 cup of chocolate chips in a glass bowl in the microwave; cool slightly. Stir in about 1 cup of the cheesecake batter till well combined.
Pour the plain batter into the unbaked crust. Drop spoonfuls of the chocolate batter randomly over the plain batter. Swirl with a butter knife or the handle of a wooden spoon.
Bake in a 325° oven for 70-80 minutes. Cool completely, then chill for at least 4 hours or overnight.
Before serving, sprinkle chocolate chips and pecans over the top and drizzle with caramel sauce.