Should I give my ex boyfriend this back?

My boyfriend and I recently broke up. A few months ago he gave me this necklace with his fraternity letters on it as a symbol of his love and commitment to him. But he called me a week ago and I was hoping he was calling to say he wanted to get back together but it turns out he just wants the necklace back. And he's been calling non stop about it but it was a gift and something I want to keep to remember the relationship by. He's becoming really pathetic about the whole thing which makes me want to keep it more. But should I give it back though