Flatten the chicken so each piece is even in thickness. Cover with plastic wrap and gently pound with a meat mallet or the bottom of a measuring glass.
In a measuring cup, stir together the salt and water until fully dissolved. Place chicken breasts in a 9×13 pan in a single layer and pour the brine over them. Let sit for 15 minutes. (Note: You can brine up to 4 hours if desired.)
Remove chicken from the brine and pat completely dry with paper towels.
Heat oil in a frying pan over medium-high heat, coating the bottom of the pan.
Place chicken breasts in the pan. Reduce heat to medium and cook for 1 minute without moving.
Flip the chicken over and cook for 1 minute more without moving.
Flip the chicken, cover the pan with a tight-fitting lid, reduce heat to low, and cook for 10 minutes undisturbed. Do not lift the lid during this time.
Flip the chicken again, turn off the heat, and remove the pan from the burner. Let it sit covered for another 10 minutes, still without lifting the lid.
After resting, check for doneness. If any pink remains, cover again and let sit for a few more minutes.
Optional: If you like your chicken to be grilled, you can broil or put on the grill for a few minutes on each side however this will take away some of the moistness
