01 - Whisk together olive oil, lemon juice, lemon zest, garlic, parsley, thyme, salt, and pepper in a bowl until fully combined.
02 - Place chicken breasts in a shallow dish or resealable bag. Pour marinade over chicken, turning to coat evenly. Cover and refrigerate for 30 minutes.
03 - Trim woody ends from asparagus stalks. Using a vegetable peeler, shave each stalk lengthwise into thin ribbons. Place ribbons in a bowl.
04 - Drizzle shaved asparagus with olive oil and lemon juice. Toss gently to coat evenly. Season with salt and pepper to taste. Set aside until serving.
05 - Preheat grill or grill pan to medium-high heat, approximately 375-400°F.
06 - Remove chicken from marinade, allowing excess to drip off. Grill for 6-7 minutes per side until internal temperature reaches 165°F. Transfer to a plate and let rest for 5 minutes.
07 - Arrange shaved asparagus on serving plates. Place rested chicken breasts on top. Garnish with shaved Parmesan if desired. Serve immediately.