How to Make It
Cut kernels from corncobs (about 2 1⁄4 cups); place in a bowl. Using the large holes on a box grater, scrape pulp and liquid (about 1⁄2 cup) from cobs into bowl with kernels. Discard cobs.
Heat butter in a large saucepan over medium-high. Add onion and garlic; cook, stirring occasionally, until softened, 3 to 4 minutes. Stir in chicken broth, potatoes, salt, and pepper. Bring to a boil. Reduce heat to medium-low; cook, stirring occasionally, until potatoes are just tender, 12 to 15 minutes. Add corn mixture; stir until well combined.
Transfer 1 cup of the chowder to a blender. Secure lid on blender, and remove center piece to allow steam to escape. Place a clean towel over opening. Process until smooth, about 15 seconds. Stir mixture back into remaining chowder. Bring to a simmer over medium. Add shrimp, and cook, stirring occasionally, until opaque and cooked through, about 3 minutes. Stir in heavy cream. Ladle into 4 bowls. Sprinkle each serving with chives.