Whisk the olive oil, minced garlic, balsamic vinegar, lemon juice, dried oregano, cumin, dried basil, onion powder, sugar, salt, pepper, and paprika together in a large resealable freezer bag or bowl to make the marinade.
Add the pounded chicken breasts to the bag or bowl, seal or cover, and refrigerate to marinate for 4–8 hours.
About 20–30 minutes before cooking, remove the chicken from the refrigerator and let it sit at room temperature.
To cook on the stovetop: heat 1 tablespoon of olive oil in a large nonstick skillet over medium-high heat until very hot. Remove chicken from the marinade, drain and pat dry, then place in the skillet.
Cook undisturbed for 3–4 minutes until nicely browned, then flip, cover, reduce heat to medium, and cook another 4–6 minutes until cooked through. Transfer to a cutting board and let rest 5 minutes before slicing.
To cook on the grill: preheat the grill to medium (375–450°F). Grease the grates lightly, drain and pat dry the marinated chicken, then grill undisturbed for 5–7 minutes per side until an instant-read thermometer registers 165°F. Let rest 5 minutes before slicing.
