Boil a large pot of salted water and cook pasta according to package directions until al dente.
Heat olive oil in a large skillet over medium-high heat.
Add chicken breast, salt, pepper, and oregano; cook until golden brown and internal temperature reaches 165F (74C).
Reduce heat to medium, add minced garlic, and sauté for 60 seconds until fragrant.
Pour in heavy cream and bring to a gentle simmer.
Gradually whisk in Parmesan cheese until melted and the sauce thickens.
Reserve 0.5 cup of pasta water, then drain the pasta.
Toss pasta into the skillet with the sauce and chicken, adding reserved pasta water as needed for consistency.
Garnish with fresh parsley and serve immediately.