In a large bowl, mix together the kosher salt and granulated sugar in the cold water until fully dissolved.
Submerge the chicken breasts in the brine, cover the bowl, and place it in the refrigerator for four hours.
After brining, rinse the chicken breasts under cold water for about 30 seconds to remove excess salt and sugar.
Pat the chicken dry thoroughly with paper towels.
Heat a skillet over medium-high heat and add the neutral oil.
Sear the chicken breasts in the hot skillet for three minutes on each side until they are golden brown and cooked through.
