I feel exactly how you feel.
I mean, you can't help but feel sorry for them, but at the same time, you got to think of your safety. As well as that, it gets annoying when you got people doing that. Usually I tell them no (I live in Compton and most seem to be drugged out) that I don't have any money, but often they'll catch me right on my way out of the store when I barely have put my money in my pocket.
Just as everyone else said, be cautious, and do call the store manager. You have the right to go to a store without feeling scared or being harassed, and yes, it is harassment in the way that many of them do, especially that guy, asking for chicken and acting like any other food would be just cruel to give.
At our Wal-Marts here, in Southern California, even as bad as our economy is, I hardly see any panhandlers at our stores. I suppose that many of them think that only stingy rich people shop there. lol