Preheat oven to 425°F (220°C). Place a wire rack over a rimmed baking sheet (or line a baking tray with parchment if no rack).
Pat the chicken breasts dry thoroughly with paper towels — this helps skin crisp beautifully.
In a small bowl, combine softened butter, lemon zest, lemon juice, minced garlic, thyme, rosemary, salt, and pepper. Mix until smooth and well blended.
Gently slide your fingers under the skin on each chicken breast (without tearing), and tuck about 1 tablespoon of the lemon-garlic butter mixture under the skin, spreading gently so it coats the meat underneath.
Brush the olive oil over the chicken skin, then pat lightly with a pinch more salt and pepper.
Place the chicken breasts skin-side up on the rack on the baking sheet. Roast in the preheated oven for ~45–60 minutes — check after 40 minutes, then every 5–10 minutes depending on size. The chicken is done when skin is golden-brown and a meat thermometer inserted at the thickest part (but not touching bone) reads ~162–165°F (72–74°C).
Remove from oven and let rest 5–10 minutes before serving — this helps juices redistribute and keeps meat moist.
Serve hot, optionally with lemon wedges and a sprinkle of fresh parsley or thyme for brightness.