1. Participants must be ≥ 3 to < 18 years of age at enrollment 2. A confirmed genetic diagnosis of HCH 3. A height Z score of ≤ - 2.0 standard deviations (SDs) in reference to the general population of the same age and sex, as calculated using the Center for Disease Control and Prevention (CDC) growth charts 4. Males and females are eligible to participate in this clinical study. 5. Females ≥ 10 years old or who have begun menses must have a negative pregnancy test at the Screening Visit and be willing to have additional pregnancy tests during the study. 6. If sexually active, participants must be willing to use a highly effective method of contraception while participating in the study.

1. Short stature condition other than HCH
2. Have an unstable condition likely to require surgical intervention during the study.
3. Evidence of decreased growth velocity and/or growth plate closure
4. Taking any of the prohibited medications
5. Treated with growth hormone, insulin-like growth factor 1 (IGF-1), or anabolic steroids
6. Planned or expected to have limb-lengthening surgery during the study period.
7. Planned or expected bone-related surgery (ie, surgery involving disruption of bone cortex, excluding tooth extraction), during the study period
8. Require any investigational agent prior to completion of study period.
9. Received vosoritide or another investigational product or investigational medical device in the past
10. Have used any investigational product or investigational medical device for the treatment of HCH or short stature at any time, including vosoritide
11. Have current malignancy, history of malignancy, or currently under work-up for suspected malignancy.
12. Have known hypersensitivity to vosoritide or its excipients.
13. Concurrent disease or condition that, in the view of the investigator, would interfere with study participation or safety evaluations, for any reason