"I like chicken cuisine the most."
鶏肉(とりにく)料理(りょうり)が私(わたし)は一番好きです. It was mark wrong? Must watashi always be in front?
Unless you're introducing a new topic, having a は after a が in a sentence is bad Japanese and it should never be done.
I mean, が can be a part of the topic and therefore be placed before the は in a sentence and it would be correct, but, the way you wanna use it in your sentence is incorrect. Just place the 私 at the beginning or omit it completely.
"Chicken cuisine" is a bit odd, no? I would probably say "chicken dishes" or "meals/dishes with chicken"