Pat the chicken breasts dry with paper towels and season both sides with kosher salt and black pepper.
Heat the butter and olive oil together in a large skillet over medium-high heat until the butter is melted and foamy.
Add the chicken breasts to the skillet and cook for 5-6 minutes on each side, or until golden brown and cooked through (internal temperature should reach 165°F). Remove the chicken from the skillet and set aside.
Reduce the heat to medium. Add the minced garlic to the skillet and sauté for 30 seconds until fragrant, stirring constantly to avoid burning.
Add the orzo pasta to the skillet and stir to coat it in the garlic butter mixture. Cook for 1 minute.
Pour in the chicken broth and bring the mixture to a boil. Reduce heat to low, cover, and simmer for 10-12 minutes, or until the orzo is tender and most of the liquid is absorbed.
Stir in the Parmesan cheese, lemon zest, and lemon juice until the cheese is melted and the orzo is creamy.
Return the cooked chicken breasts to the skillet, nestling them into the orzo. Cook for an additional 2 minutes to warm the chicken through.
Sprinkle the chopped fresh parsley over the dish before serving.