Just had a very extensive conversation with a native speaker, and "Letʻs eat the barbecued chicken" should also be an acceptable answer. (i.e., it is fine to use the article ʻtheʻ in the translation as it may very well enhance communication in the context of the conversation.)
My response was: Let's eat the barbecued chicken.
I was given this message in response to my answer:
You have a typo. Let's eat barbecued chicken.