Season both sides of the chicken breasts with salt and black pepper.
Heat olive oil and 1 tablespoon of butter in a large skillet over medium-high 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 reaches 165°F). Remove the chicken from the skillet and set aside on a plate.
Reduce heat to medium and add the remaining 2 tablespoons of butter to the skillet. Once melted, add the minced garlic and cook for 1 minute until fragrant.
Stir in the Dijon mustard, lemon zest, and lemon juice. Mix well to combine.
Add the orzo pasta to the skillet and stir to coat in the lemon butter Dijon sauce.
Pour in the chicken broth and bring 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.
While the orzo cooks, prepare the feta sauce by mixing the crumbled feta cheese and Greek yogurt in a small bowl until smooth and creamy.
Return the cooked chicken breasts to the skillet, nestling them into the orzo. Spoon some of the sauce over the chicken and cover for 2 minutes to warm through.
Sprinkle chopped fresh parsley over the dish before serving.
Serve the chicken and orzo hot with a dollop of the feta sauce on top or on the side.