The purpose of this study is to further evaluate the effects that eltrombopag has on platelets in subjects with chronic ITP. Eltrombopag is approved by the Food and Drug Administration (FDA) for the treatment of low platelets in patients with chronic ITP. It is being further studied by GlaxoSmithKline in other conditions associated with low platelets. This research study is being done because eltrombopag has been shown to increase platelet counts in a different way than other therapies for ITP. The investigators want to further study how eltrombopag affects subjects and their platelets to determine how the study drug should best be used in ITP treatment.