Pat the chicken breasts dry with paper towels. Season both sides with kosher salt and black pepper.
Heat the butter and olive oil in a large skillet over medium heat until melted and hot.
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 165°F). Remove the chicken from the skillet and set aside on a plate.
Reduce the heat to medium-low and add the minced garlic to the skillet. Cook for about 30 seconds until fragrant, stirring constantly to avoid burning.
Add the orzo pasta to the skillet and stir to coat it in the butter and garlic mixture.
Pour in the chicken broth and water, then add the lemon zest and lemon juice. Stir to combine and bring the mixture to a simmer.
Cover the skillet with a lid and cook for 10-12 minutes, stirring occasionally, until the orzo is tender and most of the liquid is absorbed.
Stir in the grated Parmesan cheese until melted and creamy.
Return the cooked chicken breasts to the skillet, nestling them into the orzo. Cook for an additional 2 minutes to reheat the chicken and allow flavors to meld.
Sprinkle the chopped fresh parsley over the dish before serving.