In a large pot, heat olive oil over medium heat. Add the diced chicken and season with salt, pepper, and oregano. Cook until the chicken is golden brown and cooked through, about 5-7 minutes.
Remove the chicken from the pot and set it aside. In the same pot, add minced garlic and red pepper flakes (if using); sauté for about 1 minute until fragrant.
Stir in the crushed tomatoes and chicken broth, bringing the mixture to a simmer.
Add the orzo pasta to the pot and stir well. Cook according to package directions, typically 8-10 minutes, until the orzo is al dente.
Reduce the heat to low, then stir in heavy cream and Parmesan cheese, mixing until combined and creamy.
Return the cooked chicken to the pot and stir in fresh basil. Allow everything to warm together for a couple of minutes, adjust seasoning with salt and pepper.
Serve immediately, garnishing with additional basil and Parmesan if desired.