Cut kernels from corn cobs to measure about 4 cups. Using the dull side of a knife blade, scrape liquid from corn cobs directly into a 6-quart slow cooker. Add cobs and 3 cups kernels. Stir in chicken stock, thyme, 1 teaspoon salt, and potatoes. Cover and cook on LOW for 7 hours and 30 minutes.

Discard cobs. Stir half-and-half and 2 tablespoons butter into corn mixture. Transfer half of corn mixture to a blender. Remove center piece of blender lid (to allow steam to escape); secure lid on blender. Place a clean towel over opening in lid (to avoid splatters). Process until smooth. Pour into a large bowl. Repeat procedure with remaining corn mixture. Stir in pepper.

Melt remaining 2 tablespoons butter in a large skillet over medium heat; cook 2 minutes or until foamy. Add shrimp, remaining 1 cup corn kernels, and remaining 1/2 teaspoon salt to pan; cook 4 minutes or until shrimp turn pink and are done, stirring occasionally. Stir in 1 1/2 tablespoons chives. Divide soup among 10 shallow bowls; top evenly with shrimp mixture, and sprinkle with remaining 1 1/2 tablespoons chives.