The study is an open-label, sequential cohort, dose-escalation study of BMN 111 in children who are between five and 14 years old. The primary objective is to assess the safety and tolerability of daily subcutaneous doses of BMN 111 administered for six months. The secondary objectives will include an evaluation of change in annualized growth velocity, changes in absolute growth parameters, changes in body proportions and other medically relevant and functional aspects of achondroplasia, such as sleep apnea and joint range of motion. Prior to enrolling in the Phase II study, all patients will have participated in a six-month natural history study to determine baseline growth velocity data. This is an international study that will enroll approximately 24 subjects for a treatment duration of six months.