Preheat oven to 350°F. Grease a deep 9x13-inch baking dish (at least 2 inches deep). If you're not sure your pan is deep enough, set it on a rimmed baking sheet to catch any overflow.
Spread the coconut and pecans in an even layer across the bottom of the prepared dish.
Prepare the cake mix according to package instructions.
Pour the batter evenly over the coconut and pecan layer.
In a separate bowl, use an electric mixer to beat together the softened butter, cream cheese, and vanilla extract until smooth. Gradually add the confectioner's sugar and mix until fully incorporated.
Dollop the cream cheese mixture over the top of the batter in spoonfuls.
Use a knife to gently swirl it in with a few slow passes. Don't over-swirl or you'll lose the ribbon effect.
Scatter the chocolate chips evenly over the top.
Bake for 40 to 45 minutes. Do not use a toothpick to test for doneness. Instead, gently press the center of the cake with your fingers. When the chocolate cake portion springs back and feels set, the cake is ready, even if there's still a slight jiggle. The inside will be gooey by design.
Cool in the pan before slicing. For neat squares, let it cool completely. For a warm, gooey serving, slice after about 20 minutes and serve with a scoop of vanilla ice cream.