Actually, taking it away is a BAD idea

The reason she is nipping is because she knows you will take it away and she won't get it back. Taking it away only reinforces that idea and makes her MORE possessive and aggressive.

Instead, when she has something that you don't want her to have, take it away but give her something instead that is equally as good if not better. You can also practice "the exchange game" by just taking something away, but immediately giving it back. Do this a couple times a day. Or, if it is so extreme she won't let you near, instead of physically taking it, just walk by and drop treats to her if she doesn't growl. Once she lets you walk by withough growling or even thinking you may take it away, start bending down. Throw a treat to her. Do this multiple times a day. This should progress from there until you have a dog that will actualy WANT to give things up in hopes that it will get something better in return!

Now, don't expect this to happen fast. This will take alot of TIME and dedication to training. Be consistant and fair.