Cut each breast in half horizontally so you have 4 chicken cutlets. Use a meat mallet to pound each cutlet out to about 1/2-inch thickness. Season chicken cutlets well on both sides with salt and pepper then dredge in flour, shaking off excess.
Heat a large high-walled stainless steel skillet over medium-high heat Add 1 tablespoon butter and 1 tablespoon olive oil and swirl to coat pan. Add chicken cutlets in a single layer, sear 3-4 minutes on first side, then flip to opposite side and add remaining 1 tablespoon butter. Cook an additional 3-4 minutes on opposite side until chicken is golden brown and registers 165F.
Transfer chicken to a cutting board, allow to cool slightly, then cut into 1-inch cubes. Set aside.
Set same pan to heat over medium heat. Add remaining 1 tablespoon olive oil and swirl to coat pan. Add onion and orzo and cook 3-4 minutes until orzo is a light golden brown and onion is translucent. Add garlic and cook 1 minute until fragrant.
Pour white wine into pan and use a wooden spoon to scrape up any browned bits. Allow wine to simmer 2-3 minutes at medium heat, stirring occasionally, until wine is reduced in half.
Pour chicken broth into pan and bring to a simmer over medium-high heat. Reduce heat to medium-low and simmer orzo uncovered for 8-10 minutes stirring occasionally until orzo is tender and most of liquid is evaporated.
Toss cubed chicken, lemon juice, zest, capers, and parsley into orzo. Season orzo with salt and pepper to taste as needed and serve warm. Enjoy!