Hey! Check out this brain teaser. Who's got the coin?

Q: A wealthy merchant explores a mysterious island with three wise locals. The merchant angrily accuses one local of stealing his gold coin. The coin is in one of the three locals' hands. Each local either always tells the truth or always lies, but never both. The first local says, 'I don't have the coin.' The second local says, 'I truly don't have the coin.' The third local remains silent. Who has the coin?

Ask me Yes/No questions to solve this puzzle!