The purpose of this study is to evaluate the safety and tolerability of romiplostim (AMG 531) in the treatment of thrombocytopenia in pediatric subjects with chronic ITP. We will also evaluate the efficacy of romiplostim (AMG 531) and characterize the pharmacokinetics of romiplostim (AMG 531). It is anticipated that romiplostim (AMG 531), when given at an effective dose and schedule, will be well tolerated treatment for thrombocytopenia among pediatric subjects with chronic ITP.