Bring a large pot of salted water to a boil. Add the pasta and cook according to package directions until al dente. Once cooked, drain and set aside, reserving about 1/2 cup of pasta water for later.
Heat olive oil in a large skillet over medium-high heat. Add the diced chicken breast and season lightly with salt and pepper. Cook for about 5-7 minutes, stirring occasionally, until the chicken is browned and cooked through. Remove the chicken from the skillet and set aside.
In the same skillet, add the minced garlic and cook for 30 seconds until fragrant. Pour in the crushed tomatoes, stirring to deglaze the pan and pick up any browned bits. Let this simmer for about 5 minutes to deepen the flavor.
Lower the heat to medium-low and stir in the heavy cream and dried basil. Season with salt and black pepper. Let the sauce simmer gently for another 3-4 minutes until it thickens slightly.
Return the cooked chicken to the skillet, stirring it into the sauce. Add the drained pasta and toss everything together until the pasta is well coated. If the sauce feels too thick, gradually add some reserved pasta water to loosen it to your preferred consistency.
Serve the pasta hot, garnished with fresh basil leaves and a generous sprinkle of Parmesan cheese. Enjoy immediately with your favorite salad or garlic bread.