Bring a large pot of salted water to a boil. Add the tagliatelle and cook according to package directions until al dente. Drain and set aside.

While the water heats, pat the chicken dry and season with 1/4 tsp salt and 1/4 tsp black pepper.

Heat the olive oil in a large skillet over medium-high heat. Add the chicken in an even layer and cook, stirring occasionally, for 5 to 7 minutes until lightly browned and cooked through.

Add the sliced onion and minced garlic to the skillet with the chicken. Cook for 2 to 3 minutes, stirring, until the onion is soft and translucent.

Add the red, green, and yellow bell pepper strips. Reduce the heat to medium and cook for about 5 minutes, stirring, until the peppers are tender but still slightly crisp.

Pour in the heavy cream and stir to combine with the chicken and vegetables. Bring to a gentle simmer.

Add the grated parmesan cheese and stir constantly until the cheese is melted and the sauce is smooth and slightly thickened, about 2 to 3 minutes.

Add the cooked tagliatelle to the skillet. Toss gently until all the pasta is well coated in the creamy sauce. Season with the remaining salt and black pepper to taste.

Remove from the heat and let sit for 1 to 2 minutes to allow the sauce to cling to the pasta. Serve immediately, topped with fresh basil if using.