Pete will occasionally do this as well. He doesnt do it with normal food or treats, but if he gets something he's not supposed to have (usually because it could be dangerous for him to eat) he will growl and nip if I try to get it back. The other thing that worry's me about going after it is then he try's to swallow it without chewing and this can be even more dangerous. Luckily we've learned to tell him drop it and then ask if he wants a treat and he usually will, he's getting better. I heard of someone else on here talk about when their dog got something they werent supposed to she'd quickly grab a treat and say "deal or no deal" and their dog would drop what they had and go for the treat.
Good Luck