The best bank for immigrants is one that accepts other forms of identification instead of a Social Security Number. An undocumented immigrant may need an Individual Taxpayer Identification Number (ITIN) to open an account at some financial institutions. Chase is a good option for immigrants without a SSN or ITIN because the bank will accept a passport with a photo, a Matricula Consular card, or a U.S. Employment Authorization card (with photo) as a primary form of identification.