To prepare the dressing, place the blue cheese, buttermilk, and olive oil in a medium bowl and stir together with a fork, mashing a little to break up the cheese. Season with the lemon juice, salt, pepper, and chives. Set aside.
Wash the tomatoes, and pat dry with a paper towel. Slice each tomato in half lengthwise and season with a pinch of salt. Add the tomatoes to the dressing mixture and toss to combine then garnish with freshly ground pepper, to taste.