Pat the chicken dry with paper towels and then sprinkle with salt and pepper and dredge in the flour.
Heat a 10-inch skillet over medium high heat and add the oil. Dust off the excess flour and add the chicken to the pan. Cook on one side for 3 minutes, then turn each breast over and lower the heat to medium and cook for 4 minutes. The chicken should be golden brown, but will still be raw inside.
Add sliced garlic, tomatoes, and white wine. Cook until the wine has evaporated, about 3 minutes. Add the chicken stock, heavy cream, salt, and pepper. Cook for about 5 minutes until the sauce is thickened and the chicken registers 165 degrees F internal temperature.
Turn off the heat and stir in the basil and vinegar. Taste the sauce and season with salt and pepper if needed.
Serve the chicken with the sauce.
