This is an open-label study using alefacept in the treatment of patients with chronic plaque psoriasis who have not responded to treatment with an anti-TNF agent. Patients not responding to Enbrel® 50 mg weekly with a 75% reduction of Psoriasis Area and Severity Index (PASI) Score or a Physician Global Assessment (PGA) score of 'almost clear' or 'clear', will be treated with 15 mg alefacept intramuscularly (IM) once weekly for up to 20 weeks. Patients who have 'cleared' or 'almost cleared' at the end of 12 weeks of treatment with alefacept will have completed the 'standard treatment' phase of the study. Study subjects who have not responded to treatment during the initial 12 weeks will continue with alefacept therapy for an additional 8 weekly doses or until the subject has reached a PGA of 'almost clear' or 'clear'. Alefacept is FDA approved for this indication for 12 weeks of treatment and this clinical trial is extending the treatment window for up to 8 additional weeks. Because of this increased exposure to alefacept, all subjects will be carefully monitored while on treatment and followed post-treatment at 3, 4, 6, 9 and 12 months after the last dose of alefacept is given.