If you were terminated due to a ticket you received on duty and was found under the influence or it is a required condition of employment to maintain a clean license, then no, you can not. Due to the reason being, it is justifiable by the employer. Keep in mind, unemployment will contact the employer and that is how it is determined if you will receive unemployment. If your termination was unjustifiable and not due to the DUI, then yes, you may file for unemployment, but it can still be denied, then you would have to file an appeal.