Heat up about a cup of water in the microwave or stovetop until warm. The idea is to heat it enough to dissolve the sugar and salt, not boil it. Remove from heat and pour in the salt and sugar. Stir until salt and sugar dissolve.
Let the salt and sugar brine cool, then add the remaining water and apple cider. The water should not be warm - you want it completely cool.
Put the chicken breasts in a non-reactive pot or container and pour the brine over them. Then add garlic, thyme, bay leaves, peppercorns, pepper flakes, and the orange and lemon slices.
Cover the pot or container with a lid, and place it in the fridge for 45 minutes to an hour. Try not to let it brine for more than an hour.
Remove the chicken breasts from your brine and dry them with paper towels.
Brush with butter and rub with your favorite seasoning, and they're now ready to grill, roast, bake, or smoke.