Prepare grill for direct/indirect cooking. Target temperature in the grill is 400 degrees measured on indirect side.
Remove giblets from chicken, and pat dry. Lightly oil the chicken including the cavity. Apply dry rub liberally, including inside the cavity.
Open the can of wine. You will insert the can into the cavity of the chicken, but do so slowly so the can does not tip. To do this, gently lower the chicken over the can into the cavity, the drumsticks will act like legs of a stool, with the can being the third leg.
Place the chicken on the grill over indirect side with breast facing the heat side. Insert a digital meat probe if you have one. Be sure the drumsticks are positioned to prop the bird and avoid tipping.
Cover and grill until the internal temperature of the breast and thigh are 160 degrees Fahrenheit. Can take 30 to 40 minutes depending on your cooker, the finished temperature is the most important.
If your grill is smaller and you notice too much browning on the breast before it is done, rotate the bird 180 degrees so the breast faces away from you. Although be careful to not spill the wine or let it fall over.