Pat the chicken breasts dry with paper towels and season both sides generously with salt and pepper. Mince the garlic, zest the lemon, and chop the fresh dill.
Heat the olive oil in a large skillet over medium-high heat. Add the chicken breasts and cook for 5-6 minutes per side until golden brown and cooked through. Remove chicken and set aside tented with foil.
Lower heat to medium and add minced garlic to the skillet. Sauté for about 30 seconds until fragrant, careful not to burn.
Pour in the heavy cream, stirring to incorporate browned bits. Add lemon juice and lemon zest, stirring to blend into a smooth sauce.
Sprinkle chopped dill into the sauce and stir well. Let simmer gently for 3-4 minutes to thicken and meld flavors.
Return chicken breasts to the skillet, spoon sauce over each piece. Simmer for 2-3 minutes to heat through and absorb flavors. Adjust seasoning with salt and pepper if needed.
Plate the chicken and spoon extra sauce over the top. Serve with your choice of sides like steamed vegetables, rice, or mashed potatoes.
