In Chinese grammar both又and再 are used to expressthe repetition of an action,but with different meanings.
1.又indicates that the action or situation has repeated .
ex.他今天又去学校了(He went to school yesterday.He has gone to school today.)
ex.我上星期生病了，这星期我又生病了。(I was sick last week.This week I've been sick again.)
ex.昨天下午下雨了，今天早上又下了。(It rained yesterday afternoon.This morning it rained again.)
Note：又indicates that the action or situation is definitely going to recur.
ex.明天又是星期天。(It is Sunday tomorrow .)
ex.又快到圣诞节了。(Christmas comes soon again.)
2.再indicates that the action is going to recur.
ex.我不想再看见他了。(I don't want to see him again.)
ex.下星期我再去香港。(I will go to HongKong again next week.)
3.Apparently your example indicates that the action of "来 "is going to recur.So the answer should be 麻烦你再来一份鸡肉.
Try to distinguish the example.
(He comes again,but I don't want to meet him.If he comes again tomorrow, you just tell him I'm not here.)