Prepare an ice water bath. Bring 8 cups water to boil in a large pot. Reduce heat to medium low. Plunge lobster into water, headfirst, and simmer,covered, for 9 minutes. (Do not let water boil.) Transfer to ice water bath using tongs; reserve cooking liquid. Let stand for 10 minutes to cool.

Crack lobster claws, knuckles, and tail, and remove meat; reserve shells and body. Coarsely chop meat. Refrigerate until ready to use.

Return shells and body to pot with cooking liquid (For added flavor, chop body with a cleaver before returning to pot.) Add reserved cobs. Simmer, covered, over medium heat for 35 minutes. Strain stock through a fine sieve into a bowl; discard solids.

Heat oil in a medium saucepan over medium heat. Cook corn kernels, onion, garlic, and 3/4 teaspoon salt, covered, stirring occasionally, until tender, about 20 minutes.

Strain soup through sieve. Set aside 1 1/2 cups corn mixture. Working in batches, puree remaining corn mixture and strained liquid in a blender until smooth. Strain soup through sieve, and return to pot with reserved corn and lobster meat. Cook over medium heat until warmed through. Stir in chives, 1/4 teaspoon salt, and some pepper