Pound the chicken breasts to even them out. Season with salt and pepper.
Heat 1 tablespoon of olive oil in a large skillet on medium-high heat. Cook chicken breasts for 3-4 min per side. Transfer to a cutting board and cover.
In the same pan, heat the remaining 3 tablespoons of olive oil on medium heat.
Add onion and let it cook for 5 minutes until soft. Add garlic and cook for another 2 minutes, stirring occasionally.
Once onion and garlic are soft, pour vodka into the pan and scrape the bottom of the pan to deglaze all the tasty chicken bits that got stuck.
Crush the peeled tomatoes and add them to the pan. Let the sauce cook for 15-20 minutes or until thick and most of the water has evaporated.
Stir in heavy cream and fresh basil and let bubble. Turn the heat down to low.
Boil the pasta in salted water, according to the package’s instructions. It usually takes 10 min to cook penne pasta al dente. Reserve the pasta water.
Now, add the penne and the chicken to the sauce. Stir to coat in creamy goodness and let cook until heated through (about 1 minute).
Then add parmesan cheese and mix until luscious.
Season with salt and pepper to taste. Serve with more parmesan cheese.