Heat olive oil in a large skillet or grill pan over medium-high heat. Season the chicken breasts evenly with salt and black pepper.
Grill the chicken breasts for 5 to 7 minutes on each side until fully cooked (internal temperature of 165 F). Remove from the heat, let rest for 5 minutes, then slice into strips.
Bring a large pot of salted water to a boil. Add the penne pasta and cook according to the package instructions until al dente. Reserve 1/2 cup of pasta water, then drain the pasta.
In a large deep skillet over medium-low heat, pour in the heavy cream and let it gently simmer for 2 minutes. Whisk in the pesto sauce, grated Parmesan cheese, and red pepper flakes until smooth.
Add the drained penne pasta and sliced grilled chicken to the skillet with the creamy sauce. Toss gently to combine, adding a splash of reserved pasta water if the sauce is too thick.
Garnish with toasted pine nuts and fresh basil just before serving.