A Trial Investigating the Safety, Tolerability and Efficacy of TransCon PTH in Adults With Hypoparathyroidism

Inclusion Criteria: 1. Males and females aged ≥18 years. 2. Subjects with postsurgical chronic HP or auto-immune, genetic, or idiopathic HP for at least 26 weeks. 3. On a stable dose for at least 12 weeks (or 4 weeks if on Natpara as of September 2019) prior to Screening of: * ≥0.25 μg BID of calcitriol (active vitamin D) or ≥0.5 μg BID or ≥1.0 μg daily of alfacalcidol (active vitamin D), and * ≥400 mg BID calcium citrate or carbonate. 4. Optimization of supplements prior to randomization to achieve the target levels of: * 25(OH) vitamin D levels of 30-70 ng/mL (75-175 pmol/mL) and * Magnesium level within the normal range and * Albumin-adjusted or ionized serum calcium (sCa) level in the lower half of the normal range. 5. BMI 17-40 kg/m2 at Visit 1. 6. If ≤25 years of age, radiological evidence of epiphyseal closure based on x-ray of non-dominant wrist and hand. 7. eGFR \>30 mL/min/1.73m2 during Screening. 8. Thyroid-stimulating hormone (TSH) within normal laboratory limits within the 12 weeks prior to Visit 1; if on suppressive therapy for thyroid cancer, TSH level must be ≥0.2 μIU/mL. 9. If treated with thyroid hormone replacement therapy, the dose must be stable for at least 12 weeks prior to Visit 1. 10. Able to perform daily subcutaneous self-injections of study drug (or have a designee perform injection) via a pre-filled injection pen. 11. Written, signed, informed consent of the subject. Exclusion Criteria: 1. Known activating mutation in the calcium-sensing receptor (CaSR) gene. 2. Impaired responsiveness to PTH (pseudohypoparathyroidism) which is characterized as PTH-resistance, with elevated PTH Levels in the setting of hypocalcemia. 3. Any disease that might affect calcium metabolism or calcium-phosphate homeostasis or PTH levels other than HP, such as active hyperthyroidism; Paget's disease; hypomagnesemia; type 1 diabetes mellitus or poorly controlled type 2 diabetes mellitus; severe and chronic cardiac, liver, or renal disease; Cushing syndrome; rheumatoid arthritis; multiple myeloma; active pancreatitis; malnutrition; rickets; recent prolonged immobility; active malignancy (other than low-risk well differentiated thyroid cancer or basal cell skin cancer); parathyroid carcinoma within 5 years prior to Screening; acromegaly; multiple endocrine neoplasia types 1 and 2. 4. Use of loop diuretics, phosphate binders (other than calcium carbonate/calcium citrate), digoxin, lithium, methotrexate, or systemic corticosteroids (other than replacement therapy). 5. Use of thiazide diuretic within 4 weeks prior to the Screening 24-hour urine collection or the first dose adjustment of SOC during Screening. 6. Use of PTH-like drugs (whether commercially available or through participation in an investigational trial) including PTH(1-84), PTH(1-34), or other N-terminal fragments or analogs of PTH or PTH-related protein within 5 weeks prior to Visit 1. 7. Use of other drugs known to influence calcium and bone metabolism, such as calcitonin, fluoride tablets (\> 0.5 mg/day), strontium, or cinacalcet hydrochloride within 12 weeks prior to Visit 1. 8. Use of bisphosphonates (oral or IV) or denosumab within 2 years prior to Visit 1. 9. Non-hypocalcemic seizure disorder with a history of a seizure within 26 weeks prior to Visit 1. 10. Increased risk for osteosarcoma, such as those with Paget's disease of bone or unexplained elevations of alkaline phosphatase, open epiphyses, hereditary disorders predisposing to osteosarcoma, or with a prior history of substantial external beam or implant radiation therapy involving the skeleton. 11. Pregnant or lactating women. Note: Highly effective contraception (see Appendix 7) is required for sexually active women of childbearing potential during the trial and for 2 weeks after the last dose of study drug, and pregnancy testing will be performed throughout the trial. Sexually active women of childbearing potential who are unwilling to use highly effective contraception are excluded from the trial. 12. Diagnosis of drug or alcohol dependence within 3 years prior to Visit 1. 13. Disease processes that may adversely affect gastrointestinal absorption including but not limited to short bowel syndrome, bowel resection, gastric bypass, tropical sprue, active celiac disease, active ulcerative colitis, gastroparesis, AIRE gene mutations with malabsorption, and active Crohn's disease. 14. Chronic or severe cardiac disease within 26 weeks prior to Visit 1 including but not limited to congestive heart failure, myocardial infarction, QTcF \>430 msec (males) or \>450 msec (females), severe or uncontrolled arrhythmias, bradycardia (resting heart rate \<50 beats/minute), symptomatic hypotension, systolic BP \<80 mm Hg or diastolic \<40 mm Hg, or poorly controlled hypertension (systolic BP \>150 mm Hg or diastolic \>95 mm Hg). 15. Cerebrovascular accident within 5 years prior to Visit 1. 16. History of renal colic or acute gout within 52 weeks prior to Visit 1. 17. Any disease or condition that, in the opinion of the investigator, may make the subject unlikely to fully complete the trial, or any condition that presents undue risk from the investigational product or procedures, including treated malignancies that are likely to recur within the approximate 1-year duration of the trial. 18. Known allergy or sensitivity to PTH or any of the excipients. 19. Participation in another clinical trial in which receipt of investigational drug or device occurred within 8 weeks (or at least 5.5 times the half-life of the investigational drug) prior to Visit 1. 20. Likely to be non-compliant with respect to trial conduct.