Bring a large pot of salted water to a boil and cook rigatoni according to package instructions until al dente. Reserve 1/2 cup of pasta water before draining.
Season chicken cubes with salt, black pepper, and dried oregano.
Heat olive oil in a large skillet over medium-high heat. Sauté chicken until browned and cooked through, approximately 6 to 8 minutes. Remove chicken from skillet and set aside.
Reduce heat to medium and melt butter in the same skillet. Add minced garlic and cook for 60 seconds until fragrant.
Pour in chicken broth and simmer for 2 minutes, scraping the bottom of the pan to release browned bits.
Add cooked pasta and chicken back into the skillet.
Gradually stir in grated Parmesan cheese, adding reserved pasta water 1 tablespoon at a time until the sauce reaches the desired consistency.
Garnish with fresh parsley and serve warm.