In a small bowl, mix together the finely grated lemon peel, lemon juice, minced garlic, dried thyme, salt, and black pepper.
Place the chicken breasts in a shallow dish or resealable plastic bag. Pour the lemon marinade over the chicken, ensuring it is evenly coated. Let it marinate in the refrigerator for at least 30 minutes, or up to 4 hours for maximum flavor.
Heat the olive oil in a skillet over medium-high heat. Once hot, add the chicken breasts and cook for 5-6 minutes per side, or until they are cooked through and golden brown on the outside.
Remove the chicken from the skillet and let it rest for a few minutes.
Slice the chicken breasts and serve, garnished with chopped parsley if desired.