Season the chicken breasts with salt and black pepper on both sides.
In a large skillet, heat the olive oil over medium-high heat. Add the chicken breasts and cook for about 6-7 minutes on each side, or until golden brown and cooked through. Remove the chicken from the skillet and set aside.
In the same skillet, add the minced garlic and sauté for about 30 seconds until fragrant.
Pour in the heavy cream and chicken broth, stirring to combine. Bring the mixture to a simmer.
Add the lemon juice, lemon zest, dried thyme, and Parmesan cheese. Stir until the cheese is melted and the sauce is creamy.
Return the chicken to the skillet, spooning the sauce over the top. Let it simmer for an additional 2-3 minutes to heat through.
Garnish with chopped parsley before serving.