In a large bowl, whisk together 2 tbsp oil, 2 tbsp lime juice, 1 tsp lime zest, and all the seasonings until smooth.
Slice each chicken breast in half widthwise to make 4 thinner pieces. Lightly pound to even thickness.
Add chicken to the bowl and toss to coat. Cover and refrigerate for at least 30 minutes or up to 8–10 hours.
To grill chicken, see note 1. Otherwise, heat a large nonstick skillet over high heat. Add the remaining 1 tbsp oil. Once hot, add the chicken in a single layer.
Cook 3–4 minutes per side, or until nicely browned and cooked through (160°F or juices run clear).
Transfer to a cutting board, cover loosely with foil, and let rest for 5 minutes before slicing or dicing.
