Bring a large pot of salted water to a boil. Cook rotini according to package directions until al dente. Reserve ¼ cup pasta water, then drain.
Heat olive oil in a large skillet over medium heat. Add chicken, season lightly with salt and pepper, and cook for 4–5 minutes until golden and cooked through. Remove chicken from skillet and set aside.
In the same skillet, melt butter over medium-low heat. Add garlic and cook for 30 seconds, just until fragrant.
Stir in marinara sauce and bring to a gentle simmer. Reduce heat to low and stir in heavy cream until smooth and combined.
Add Parmesan cheese, red pepper flakes (if using), and cooked chicken. Stir until the sauce is creamy and heated through.
Add the cooked rotini to the skillet and toss to coat. Use reserved pasta water as needed to loosen the sauce.
Remove from heat and stir in fresh basil. Taste and adjust seasoning.
Serve warm with extra Parmesan and basil if desired.