Hi, Do you mean 'Advance Parol' i.e. form I-131 the travel document while your I-485 is pending? I think it depends on the service center and not local office. If you applied from Chicago should it not be in NSC? Just FYI, our 131 was filed from from VSC on Feb 07 2005 and still waiting. Their posted dates of processing is Feb 05. No news yet.
You may want to check the dates for Nebraska in that case. The local offices might issue approval only in case of emergencies, as per our attorney. They still need some written proof of emergency.
What are your case details by the way?
Thanks!