Preheat the oven to 350°F (175°C).
Pat the chicken breasts dry with paper towels and slice each in half horizontally if they are not already thin cut so you have thin fillets.
Season both sides of each chicken fillet with sea salt, dried oregano, dried dill, and black pepper.
Heat the avocado oil in a large oven-safe skillet over medium-high heat until shimmering.
Add the chicken to the hot skillet and brown 3 minutes per side; add the minced garlic to the pan during the second side so it softens and becomes fragrant without burning.
Remove the skillet from the heat and scatter the kalamata olives, sun-dried tomatoes, artichoke hearts, lemon zest, and lemon juice around and on top of the chicken.
Transfer the skillet to the preheated oven and bake 15 minutes, or until an instant-read thermometer inserted into the thickest part of the chicken reads 165°F (74°C).
Remove the pan from the oven and let the chicken rest at least 10 minutes before serving to allow the juices to redistribute.
Serve the chicken with the pan juices and Mediterranean topping.