Poke the chicken's skin with a small sharp knife. This will enable the marinade to soak in a bit.
In a large saucepan whisk together the soy sauce, water, brown sugar, grated ginger, and garlic.
Place the chicken in a large ziplock bag and pour 3/4 cup of the soy sauce mixture over the chicken. Seal the bag and shake to coat the chicken. Refrigerate for at least 1 hour or up to 1 day.
MAKE TERIYAKI SAUCE:
Place the rest of the soy sauce in a medium saucepan. Heat over high heat until it begins to boil. Then, reduce to medium-high heat and cook, occasionally whisking, until the sauce is reduced to about 2/3 cup and it has thickened, about 5-10 minutes (NOTE: The Teriyaki sauce will thicken even more as it cools).
PREHEAT GRILL AND COOK:
Preheat the grill on high heat for 10 minutes, and then reduce the heat to medium-low. Scrape the cooking grates and oil them lightly with canola oil.
Place the chicken skin-side up on the hot grill and cover the grill. Grill the chicken for 15 minutes.
Flip the chicken and cover the grill. Continue to cook the chicken until the skin is a nice deep golden color and the internal temperature reaches 160 degrees F, about another 20 minutes.
Flip the chicken over again, so the pieces are skin-side up. Use about 1/3 cup of the teriyaki sauce to brush over the chicken and cover and grill until the glaze is nice and caramelized, about 3-5 minutes.
Move the chicken to a serving platter and let it rest for 5-10 minutes before serving. Serve with remaining Teriyaki sauce.