Season your chicken with sea salt and pepper, on both sides.
Heat 1 Tablespoon of oil into a large skillet over medium-high heat. Add in your chicken filets and cook until golden-brown and cooked through about 4 minutes each side depending on thickness. Transfer to a plate, cover, and set aside.
Add in the remaining oil into your skillet and saute your tomatoes with the shallots and garlic for 2-3 minutes, or until tomatoes just begin to burst.
Pour in the wine and cook until mostly reduced around 3 minutes.
Return the chicken back into the skillet, and drizzle with your homemade pesto sauce; continue to cook for a minute more, until heated through.
Sprinkle with fresh basil and serve with lemon wedges.
Enjoy!