recruiter ask for SSN

I am apply for a position via a recruiter.But the employer asks for SSN as for the reason that recruiter told me:
"Per our discussion 1/16/09, the Social Security number is required by XXX compnay to accompany all contract assignment candidate submittals as they use it to verify that you are not a retired employee trying to return to work with them (which would violate the terms of their Early Retirement Package). However, rest assured we take our responsibility to maintain your privacy very seriously and that all information you provide will be treated with the utmost sensitivity."
the recruiter also send me the letter from the employer that asks for SSN.
Is that reasonable? do I need to send them my SSN#? I need a job urgently.
thanks,