Thank you, everyone. I see some interesting ideas here...such an eclectic group.
I did roti chicken, as well as Cornish hens, on my Genesis 1000, and they came out primo. I'm not investing in a rotisserie set-up for the kettle. As for splitting the chicken...too much work. I'll use quarters instead.
Still, all of you answered my question, and for that I am grateful. Never too much knowledge in the realm of low 'n slow, or high 'n fast.