Cut shells off crab with kitchen shears; reserve shells. Coarsely chop crabmeat; chill.
Combine shells, corn, 4 1/2 cups water, and red pepper in a saucepan; bring to a boil. Reduce heat; simmer 20 minutes or until corn is very tender. Discard shells.
Place half of corn mixture in a blender.
Remove center piece of blender lid (to allow steam to escape); secure blender lid on blender.
Place a clean towel over opening in blender lid (to avoid splatters). Process until smooth. Press pureed corn mixture through a fine sieve over a bowl, reserving liquid; discard solids. Repeat procedure with remaining corn mixture. Stir in milk, chives, and black pepper. Chill 2 hours. Top with reserved crabmeat.
