Bring a large pot three-fourths full of salted water to a boil over high heat. Add the lobsters one at a time, headfirst. Cover and cook until the lobsters are red, about 7 minutes. Transfer the lobsters to a large bowl filled with ice water and let cool completely. Remove the meat from the claws, knuckles and tails. Reserve the shells and bodies and refrigerate the meat until ready to use.

In a large pot over high heat, warm the oil. Add the reserved lobster shells and bodies and sauté until lightly browned, about 5 minutes. Add the stock, wine and corncobs, bring to a simmer and cook until reduced to about 2 1/2 cups, 25 to 30 minutes.

In a Dutch oven over medium heat, sauté the bacon, stirring occasionally, until crispy and browned, 3 to 4 minutes. Add the onion, carrots, celery and corn kernels and sauté, stirring occasionally, until tender, 4 to 5 minutes. Strain the lobster-corn stock into the Dutch oven, add the cream and bring to a simmer. Stir in the potatoes, return to a simmer and reduce the heat to medium-low. Cook until the potatoes are tender, 15 to 18 minutes. Stir in the lobster meat, salt, pepper, thyme and chives. Cook, stirring occasionally, until the lobster is heated through, 2 to 3 minutes. Taste and adjust the seasonings.

Ladle the chowder into warmed soup bowls and serve immediately. Serves 4 to 6.