Lay the breasts down on a cutting board and use a sharp knife parallel to the cutting board to slice them (carefully) in half. Season both sides with salt and pepper.
Heat the oil in a skillet or non-stick pan over medium heat and cook the chicken on both sides to an internal temperature of 160°F using a thermometer. Remove the chicken from the pan and set aside.
Add the butter, onion, and garlic to the pan; sauté for 2 minutes. Then add the tomatoes, paprika, and broth. Bring to a low simmer for 15 minutes. Season with salt and pepper to taste.
Return the chicken to the pan and stir in the sour cream and heavy cream. Bring to a simmer for 2-3 minutes while stirring occasionally.