Slice each chicken breast horizontally almost all the way through, and open up like a book. Use your hand to flatten, and season with salt and pepper.
Spread 1 tablespoon of the pesto sauce on one side of the breasts. Place 2 of the halloumi slices on top of the pesto, and fold the “plain” side over to cover. Transfer the chicken to an ovenproof baking dish and bake for 15 minutes.
Add the tomatoes and vinegar to the dish and bake for another 15 minutes. Remove from the oven and serve immediately.