It could be correct, technically. However, if the object (the chicken) is the most important information of the sentence, "lui" is skipped: (Lui) Îi dau o găină. Also correct would be: Îi dau o găină lui. The lui placed at the end implies that it is an unexpected recipient of the chicken. (It is HIM that I'm giving the chicken too, not her). If you refer to why it's hen and not chicken, I don't really agree with Duwo on this one. It might better have been a chicken, depending on the context.