Applying for food benefits after losing my job (Chicago)

I lost my job as a store manager and my household is applying for SNAP for the first time. I am in Chicago, in case local advice matters. I have a final pay stub, a termination letter and my unemployment approval. Is there an expedited option for people with very little income?

Take photos of everything you send and write down the date. I had to resend one page and the record helped.