Preheat your oven to 425°F (218°C). Remove chicken breasts from refrigerator 20-30 minutes before cooking to bring to room temperature.
Pat chicken dry with paper towels. Season both sides with salt and pepper.
If making homemade pesto: In a food processor, combine basil, Parmesan, pine nuts, and garlic. Pulse until coarsely chopped. With the processor running, slowly add olive oil in a steady stream until smooth. Add lemon juice and salt, pulse to combine.
Heat olive oil in an oven-safe skillet over medium-high heat. Once oil is shimmering, add chicken breasts and sear for 2-3 minutes on each side until golden brown.
Remove skillet from heat. Generously coat the top side of each chicken breast with 2-3 tablespoons of pesto, spreading it evenly.
Transfer the skillet to the preheated oven and bake for 12-15 minutes, depending on thickness. Do not flip the chicken during baking.
Check that the chicken is done when an instant-read thermometer inserted into the thickest part registers 163°F (73°C).
Remove from oven and loosely cover with foil. Allow to rest for 5 minutes to redistribute juices.
Slice chicken against the grain and serve with additional fresh pesto if desired.