The IMEI is not supported for an iPhone unlock

We purchased our I-phone from Best Buy about a year ago and put it on our AT&T plan. I know want to change carriers but have not been able to get AT&T to unlock it. They have referred us to Best Buy and Apple - both of whom say AT&T has to do it. AT&T message is that the IMEI is not supported for unlock. We have been getting the run around for a week - any suggestions?

[Re-Titled by Moderator]