Before I was diagnosed with celiac disease, I used to like the convenience of being able to go to Zankou Chicken. Three or four of us would get the whole chicken with garlic, pita (eek. gluten), etc.
I drove past a Zankou Chicken that is opening soon in Granada Hills (@Chatsworth and Zelzah), so I decided to check if they have gluten free options (as more places become aware of GF needs, the options available are increasing).
Lo and behold...gluten free options. Obviously, you cannot get the pita wraps, but check the link to see what you can get....the chicken is the way to go in my opinion. Their website has a handy PDF menu also.
The other place I noticed gluten free rotisserie chicken recently was Costco. Cheap, well labeled, and GF...but you have to walk the quarter mile to the meat dept in the back of the store after surviving the parking lot. The chicken is not on their website, as it is an in store item...not something that they will send via UPS...use the website to find a Costco near you, then hunt in-store. (you do need to be a member..if you live somewhere other than the US and have never heard of Costco before).
In summary, if you are a masochist, you can save some money by getting a gluten free rotisserie chicken at Costco, but for convenience and flavor Zankou Chicken is hard to beat.