We won't use present simple ("give") because it is a single action, not a repeated action or state. However, both future ("will give") and present simple ("am giving") are OK.
"Will give" is much more common. The main reason is that using future tense allows a small amount of uncertainty. I believe that he wants the chicken, and will almost definitely accept it, but there's a chance that he might say "No, I don't want it."
If I say, "I'm giving you the chicken," it is a statement of fact that cannot change. He cannot say "no." Therefore, it is a command. I am forcing him to accept the chicken.