One New Employee Act of 2011 - Amends the Internal Revenue Code to allow certain business entities, including S corporations, partnerships, trusts, estates, tax-exempt cooperatives, or sole proprietorships, a business-related tax credit for hiring individuals who received federal or state unemployment compensation for not less than one week in the one-year period prior to hiring. Limits the maximum amount of such credit for each entity to $5,000. Terminates such credit after 2016.