Create a contamination-free preparation area using dedicated gluten-free cutting boards and utensils.
Prepare brine by dissolving 1/4 cup kosher salt in 4 cups cold water. Submerge chicken breasts and refrigerate for exactly 30 minutes.
Meanwhile, whisk together olive oil, tamari/coconut aminos, lemon juice, garlic, thyme, and black pepper to create marinade.
After brining, rinse chicken thoroughly under cold water and pat completely dry with paper towels.
Place chicken in marinade, ensuring complete coverage. Refrigerate for 2 hours (minimum 30 minutes, maximum 4 hours).
Remove chicken from refrigerator 20 minutes before cooking to allow it to come to room temperature.
Heat cast iron skillet over medium-high heat until it reaches approximately 375°F (190°C). Add 1 tablespoon oil.
Place chicken presentation-side down in the skillet. Cook for 6-7 minutes without moving (for 1-inch thick breasts).
Flip chicken once and cook for an additional 5-6 minutes until internal temperature reaches precisely 165°F (74°C).
Transfer to a clean plate and tent loosely with foil. Rest for 5 minutes before serving.