Heat a large deep sauté pan over medium heat. Cut the chicken into bite-size pieces. When the skillet is hot add the butter, and the chicken. Salt and pepper liberally. Then sauté for 3-5 minutes until mostly cooked. Remove the chicken from the pan and set aside. (Do not cook the chicken all the way through yet.)
Add the pasta to the skillet and cover with 3 cups of water. Place the lid on the pan and simmer until the pasta has absorbed all the water and is almost cooked through.
Meanwhile, place the sour cream, milk, basil and garlic in the blender. Cover and puree until very smooth. Once the pasta has absorbed all the water, add the cream sauce to the pasta and stir to coat. Simmer for 2 minutes, then add the chicken back to the skillet and simmer another 2-3 minutes, until the chicken and pasta are cooked through and the sauce has tightened a little. Salt and pepper to taste.
Remove the skillet from heat. The sauce will continue to thicken as it cools. Toss well, then add the tomato halves to the pasta. Serve immediately.