Begin by seasoning the chicken breasts generously with salt and black pepper on both sides.
In a large skillet, heat the olive oil over medium-high heat. Once the oil is hot, add the seasoned chicken breasts. Sear them for about 5-6 minutes on each side or until they are golden brown and cooked through. Remove the chicken from the skillet and set it aside on a plate.
In the same skillet, add the diced onion and cook for 2-3 minutes until it becomes translucent. Then, add the minced garlic and chopped rosemary, cooking for an additional minute until fragrant.
Zest one lemon and then juice both lemons, adding the juice to the skillet. Pour in the chicken broth and bring the mixture to a simmer.
Reduce the heat to low, and stir in the heavy cream. Return the chicken breasts to the skillet, spooning the sauce over them. Let everything simmer together for another 3-4 minutes.
Finally, add the cubed butter to the skillet. Stir gently until the butter melts and the sauce becomes rich and creamy. Taste and adjust seasoning if necessary.
Serve your Skillet Creamy Lemon Rosemary Chicken over fluffy rice if desired, spooning the luscious sauce generously over the top. Garnish with additional fresh rosemary or lemon zest for an extra pop of flavor!