In a large skillet over medium-high heat, add olive oil. Once shimmering, add diced chicken breast, seasoning with salt and pepper. Sauté for about 6–8 minutes until golden brown and cooked through. Transfer chicken to a plate, leaving drippings in the pan.

Reduce heat to medium and add heavy cream to the same skillet, scraping up brown bits. Stir in cayenne pepper and Parmesan cheese, mixing well until cheese melts and sauce thickens, approximately 3–5 minutes.

While sauce simmers, bring a large pot of salted water to a boil. Cook linguine according to package instructions until al dente, about 8–10 minutes. Reserve about ½ cup of pasta water before draining.

Return sautéed chicken to skillet with the creamy sauce, stirring to combine. Gradually toss in drained linguine, ensuring each strand is coated. Add reserved pasta water as needed for desired sauce consistency.

Serve hot, garnished with additional Parmesan cheese and fresh herbs if desired. A drizzle of olive oil can enhance flavors.