I have a Showtime Rotisserie, too and it is GREAT! Dinner and a show, literally!
Did yours come with the weird plastic-y gloves? If so, DO NOT LEAVE THEM ATOP THE ROTISSERIE! They will melt and you shall never remove the criminal outline of plastic from the product. Darn!

Mrs P - Yes! Also, don't hold onto any hot part for a long time. The gloves will even melt onto the spits. I use them to quickly remove the ends from the spits. To take the chicken out of the machine just use a plate. Insert the plate under the chicken and lift up. The chicken and spits will come out easily and the chicken will already be on the plate. Just place it down on a counter with two oven mitts where the ends of the spits would lay. This is by far the easiest method to remove the chicken. Next time I do this, I will take some pictures and post them.