After chemotherapy treatment, patients with AML will often have dangerously low blood counts (white cells, red cells, and platelets). In this study, we want to find out whether Eltrombopaq can help to increase the number of platelets in the blood to lower the risk of bleeding in AML patients. Patients will have received chemotherapy in the hospital (days 1-6) and are having procedures performed that would normally be done for patients receiving chemotherapy treatment. On day 14, patients will have a bone marrow biopsy that reveals that the marrow was without evidence of leukemia. Patients will receive Eltrombopaq for at least two more weeks and up to nine weeks, as long as they are benefitting from the treatment. After ending treatment patients will visit the clinic for an end of treatment visit.