Like all my chicken grilling recipes, this recipe calls for basting right before you remove the chicken from the grill. That's especially important in this case because the sugar in the glaze will burn easily if you apply it any sooner than that. Adapted from Cooks Country (a WONDERFUL magazine).
In a large bowl, combine water and soy sauce. Set aside. In a large skillet, heat oil over medium-high heat until shimmering. Add garlic and ginger and cook until fragrant, about 30 seconds. Stir into water/soy sauce mixture. Add chicken and refrigerate, covered, for at least 1 hour and up to 8 hours. Go for the full 8 hours if at all possible, but no more than that or the chicken will get too salty.
For a kettle grill: open bottom vents on grill. Light about 75 coals. When coals are covered with fine gray ash, spread evenly over bottom of grill. Set cooking grate in place and heat, about 5 minutes. For gas grill: heat all burners to medium-low. Scrape and oil cooking grate.
Remove chicken from brine and pat dry with paper towels. Arrange chicken skin-side up on grill. Grill, covered, until chicken is well browned on bottom and meat registers 120 degrees, about 25 to 30 minutes. Flip chicken skin-side down and continue to grill, covered, until skin is well browned and crisp. The meat should register 170 to 175 degrees, about 20 to 25 minutes longer. Apply glaze several minutes before removing chicken from grill.
You can make the chicken to this point up to 2 hours before serving. Transfer to a large disposable aluminum serving tray, cover with foil and hold in a 200 degree (warm) oven.