Can AT&T unlock a previously Purchased iPhone?

Will AT&T unlock my iPhone if it is under contract and sold to a new owner… Its an iPhone 4 black through AT&T.

You can try making a request with AT&T. But i don't think they will unlock it if it is under contract. And also they would ask for original owner's information. If you are not able to unlock it successfully through them, You can go on with any trusted private unlocking service. For example, You can unlock your iPhone through remote unlocking service. You can get the remote unlocking service for an iPhone from http://www.wickedunlock.com/apple-iphone-4/rs11wp9/ at affordable cost. This method of unlocking doesn't require a Jailbreak too.
Here are the steps for unlocking an iPhone 4,
1. Wait for us to send you an email saying your phone has been activated or remotely unlocked.
2. Install the latest version of iTunes.
3. Make sure your Apple iPhone 4 phone software is updated to the latest version using the iTunes software.
4. Connect your Apple iPhone 4 to iTunes with a NOT ACCEPTED SIM card.
5. Wait until iTunes detects your Apple iPhone 4.
6. Disconnect your Apple iPhone 4 and reconnect it after 10 seconds.
7. Your Apple iPhone 4 is now unlocked.

Yes if you finished the contract.

Here are the steps for factory unlocking an iPhone for use on other carriers as well as for international travel.

1)Visit www.iphonefort-mobile.com and place an order for your iPhone to be unlocked.
2) Wait for us to send you an email saying your phone has unlocked.
3) Install the latest version of iTunes.
4) Make sure your iPhone's software is updated to the latest version using iTunes.
5) Connect your iPhone to iTunes with a NOT ACCEPTED SIM card.
6) Wait until iTunes detects your iPhone and updates.
7) Your iPhone is now unlocked and can be used with other carriers as well as internationally.

Contact At&t Service provider, may be they will help you. You can permanently Factory Unlock it online using any Trusted and reliable site.