Your best bet is to look for apartments listed on Craig's List, the Reader or Domu. They may be less likely to run a credit check because they are not spending the money (commission) to list with one of the large apartment companies or on MLS. However, it is very hard to find a landlord that will skip the credit check. You should just be up front with the landlord, explain your situation, and be prepared to come up with several months of security deposit. Put your self in the landlord's shoes. What would you be willing to do as a landlord in a similar situation?