In a medium bowl, stir together the brownie mix, eggs, vegetable oil, and water until the batter is smooth.
Spoon half of brownie batter into a lightly greased 3-quart slow cooker.
Beat cream cheese and butter at medium speed of an electric beater until creamy; gradually add sugar, beating well. Add 2 eggs, 1 at a time, beating until blended. Stir in vanilla. Fold in flour and chocolate chips.
Pour cream cheese mixture over brownie batter in slow cooker. Dollop remaining brownie batter over cream cheese mixture; swirl mixture gently with a knife.
Cover and cook on LOW setting 5 ½ hours or until set. Carefully remove the slow cooker insert from the heat element; let stand 45 minutes before serving