Preheat oven to 300ºF. On the stovetop, heat a cast iron skillet with 2 tbsp olive oil on medium heat. Add the cut tomatoes, shallots, and garlic. Season with salt and pepper. Stir and cook until the tomatoes start to soften and juice is released, about 5 minutes. Add a splash of white balsamic vinegar. Taste. Add more salt and pepper if necessary.
Remove skillet from the heat. Gently place the pieces of halibut on top of the tomato mixture and put into the oven. Cook uncovered for 15-20 minutes. Remove from the oven and let fish rest for a couple of minutes. Toss some fresh basil leaves into the pan and top with chives. Serve immediately.