Mix the water, kosher salt and sugar in a large non-reactive container.
Place chicken in the brine and refrigerate for at least 2 hours but no more than 6 hours.
Place a wire rack on a large baking sheet. Remove chicken from the brine and pat dry with paper towels. The original recipe noted that refrigerating the chicken on the rack overnight was preferred since the surface would dry more completely. If you have fridge space and time, it’s best to do this. Otherwise let the chicken dry at room temperature for 1 hour. If you refrigerated overnight, let the chicken come to room temperature.
Put the chicken in a large bowl and sprinkle with the cornstarch then drizzle the oil over it. Toss to coat the chicken well.
Preheat your grill to medium-high (about 350℉).
Place chicken on the grill skin side down and cook for 15 minutes, watching so the skin does not burn.
Turn chicken skin side up and continue cooking for 20-30 minutes, or until juices run clear.