Heat grill or grill pan to medium-high heat.
Rub chicken breasts on all sides using 2 tablespoons olive oil. Sprinkle with half of the salt and black pepper.
Place chicken on the grill and cook without moving for 3 minutes or until the edges begin to turn white. Turn the chicken one-quarter turn and continue to cook an additional 2 to 3 minutes. Flip the chicken and for 3 minutes before turning one-quarter turn and cook until the chicken reaches an internal temperature of 165 degrees. Allow the chicken to rest for at least 5 minutes. Slice before serving.
Meanwhile, cook penne according to package directions. Drain well.
As the pasta and chicken cook, prepare the vodka sauce.
In a large (12-inch) skillet over medium heat, add the remaining olive oil and butter. Allow the butter to melt and then add the garlic and onion and cook until the onion is softened.
Carefully add the vodka to the skillet (being aware of any open flames) and bring to a boil. Cook for 2 minutes.
Stir in the crushed tomatoes and remaining seasonings.
Reduce the heat to the lowest setting and stir in the heavy cream.
Add the penne to the skillet and carefully toss in the sauce. Serve topped with grilled chicken and grated parmesan cheese.