Bring a medium pot of water to a boil over high heat. Add corn and boil until cooked, approximately 5 minutes. Remove corn from pot and let cool completely. Using a sharp knife, cut corn kernels from cob.
In a medium bowl, gently stir together corn kernels, crab, lemon juice, vinegar, chives, and Cajun seasoning. Cover and refrigerate to let flavors meld, at least 1 hour and up to 1 day.
Using a small, sharp, serrated knife, cut off top third of each tomato. Using a small melon baller or strawberry huller, remove seeds from tomatoes to make cups. Trim a thin slice from bottom of each tomato cup to make them stand evenly.
Divide crab mixture among tomato cups.
Garnish with chives, if desired. Serve immediately.
