Subjects will be randomly allocated in a two to one ratio to receive treatment or placebo. All subjects in the study will receive 75 mg eltrombopag and then be randomized to receive either an additional 25 mg of eltrombopag or matching placebo tablet dispensed by the research pharmacy. Subjects and investigators will be blinded to randomization. Randomization will be stratified according to splenectomy status. Randomization will be performed at the time of informed consent with a computer generated randomization table. Subjects and investigators will be blinded to assignment and treatment in this phase. Eltrombopag will be administered for 8 weeks or until the platelet count exceeds 100,000; at this point dosing will stop, subject will be considered a responder and the subject will eligible for entering Part 2 (the long term treatment part of the study) if desired and agreed to be appropriate by the subject giving consent, and the treating physician. The dose at which the subject achieved the primary endpoint (> 50,000 and increase by > 20,000) will be considered the dose of response. Even if a patient achieves a response, if the platelet counts remains < 100,000, then the dose escalation schema in the figure above will continue.