Bring pasta water to boil and salt it. Cook pasta to al dente.
While pasta cooks, heat a large, deep skillet over medium to medium-high heat. Add extra-virgin olive oil to pan with the bacon. Cook bacon 3 minutes. Add onions and celery and cook 3 minutes more. Add bell pepper and cook another minute or two. Add flour and cook 1 to 2 minutes. Whisk in stock, then milk. When milk bubbles, add crab and corn to heat through, another minute. Stir in cheese, thyme and cayenne pepper. Melt cheese into sauce. Drain pasta and toss with cheese, crab and corn sauce. Adjust seasoning. Ladle in bowls and garnish with chives.