A Clinical Study of rhPTH(1-84) Treatment in Japanese Participants With Chronic Hypoparathyroidism

Inclusion Criteria: * The participant has signed and dated the informed consent form. * The participant is an adult male or female 20 to 85 years of age inclusive. * The participant is living in Japan and is Japanese; in this case, Japanese is defined as having been born in Japan, with Japanese parents, and Japanese maternal and paternal grandparents. * The participant has a diagnosis of chronic hypoparathyroidism with an onset of 18 months or more prior to screening. The diagnosis is based on historical biochemical evidence of hypocalcemia in the setting of a concomitant inappropriately low serum intact parathyroid hormone (PTH). If such evidence is not available the diagnosis of chronic hypoparathyroidism must be confirmed by the Shire medical monitor based on other compelling medical history. * The participant has been treated with active vitamin D therapy with alfacalcidol greater than or equal to (\>=) 1 microgram (mcg) per day (or an equivalent dose of calcitriol of \>=0.5 mcg per day or falecalcitriol \>=0.3 mcg per day) prior to baseline. * The participant has indicated a willingness and ability to perform daily subcutaneous (SC) self-injections of study medication (or will have a designee, ie, a family member or caregiver, to perform injections). * Females of childbearing potential must agree to comply with the contraceptive requirements of the protocol. * The participants who are less than (\<) 25 years old demonstrate radiological evidence of epiphyseal closure at screening based on bone age X-ray (single posteroanterior X-ray of the left wrist and hand). * The participant meets 1 of the following criteria: 1. If not receiving thyroid hormone replacement therapy, the participant has a serum thyroid stimulating hormone (TSH) level within normal laboratory limits at screening. 2. If receiving thyroid hormone replacement therapy, the dose must have been stable for at least 3 months prior to screening and serum TSH level within the reference range for the laboratory. * The participant has a 25-hydroxyvitamin D level \>=50 nanomoles per litre (nmol/L) (20 nanogram per milliliter \[ng/mL\]) and \< upper limit of normal (ULN) of the laboratory reference range. * The participant has a serum creatinine laboratory value of \<132.6 micromoles per liter (mcmoles/L) (1.5 milligram per deciliter \[mg/dL\]). * The participant has a serum magnesium level within the laboratory reference range at baseline. * The participant is not adequately controlled with standard therapy within 6 months of screening based upon the opinion of the investigator and approval by the sponsor's medical monitor. For example: 1. Hypocalcemia (albumin-corrected serum calcium \<8.0 mg/dL) or 2. Hypercalciuria (urine calcium \[mg/dL\]/creatinine \[mg/dL\] ratio \>0.4 or 24 hour urine calcium excretion \>7.5 millimoles (mmol) \[300 milligram {mg}\]/24 hours in men and \>6.25 millimoles (mmol) \[250 mg\]/24 hours in women) or, 3. Symptoms of hypoparathyroidism. Exclusion Criteria: * The participant and/or legally authorized representative(s) is unable to understand the nature, scope, and possible consequences of the study. * The participant is unable to comply with the protocol, eg, uncooperative with protocol schedule, refusal to agree to all of the study procedures, inability to return for evaluations, or is otherwise unlikely to complete the study, as determined by the investigator or the medical monitor. * The participant has any disease that might affect calcium metabolism or calcium-phosphate homeostasis other than hypoparathyroidism, such as active hyperthyroidism, Paget's disease, type 1 diabetes mellitus or poorly controlled type 2 diabetes mellitus (hemoglobin A1c \[HbA1c\] \>8%), severe and chronic cardiac, liver or renal disease, Cushing's syndrome, neuromuscular disease, rheumatoid arthritis, myeloma, pancreatitis, malnutrition, rickets, recent prolonged immobility, active malignancy, primary or secondary hyperparathyroidism, a history of parathyroid carcinoma, hypopituitarism, acromegaly, or multiple endocrine neoplasia types I and II. * The participant has a known history of hypoparathyroidism resulting from an activating mutation in the CaSR gene or impaired responsiveness to PTH (pseudohypoparathyroidism). * The participant is taking prohibited medications (listed below) or other drugs known to influence calcium and bone metabolism during their respective prohibited periods. a) The following prohibited medications should not be taken within the specified number of days prior to the first dose of rhPTH(1-84): i) 30 days: loop diuretics, thiazide diuretics, phosphate binders (other than calcium carbonate), calcitonin, cinacalcet hydrochloride. ii) 90 days: lithium. iii) 127 days: denosumab. iv) 180 days: digoxin, raloxifene hydrochloride, estrogens and progestins for hormone replacement therapy, methotrexate, systemic corticosteroids, oral bisphosphonates\*. v) 365 days: sodium fluoride, intravenous bisphosphonates\*. Note: \*The length of the washout period is dependent on the route of administration of bisphosphonate that is being used by the participant. * The participant has previous treatment or participation in an investigational trial with PTH-like drugs, including PTH(1-84), PTH(1-34) or other N terminal fragments or analogs of PTH or PTH-related protein within 6 months prior to screening. * The participant has nonhypocalcemic seizure disorder/epilepsy with a history of a seizure within the previous 6 months prior to screening; note that participant with a history of seizures due to hypocalcemia are allowed. * The participant has any disease or condition, in the opinion of the investigator, which has a high probability of precluding the participant from completing the study or that the participant cannot or will not appropriately comply with study requirements. * The participant has participated in any other investigational trial in which receipt of investigational drug or device occurred within 6 months prior to screening for this study. * The participant is pregnant or breastfeeding. * The participant has a history of diagnosed drug or alcohol dependence within the previous 3 years. * The participant has a history of gout. * The participant has disease processes that may adversely affect gastrointestinal absorption, including but not limited to short bowel syndrome, bowel resection, tropical sprue, celiac disease, ulcerative colitis, and Crohn's disease. * The participant has chronic or severe cardiac disease including, but not limited to, heart failure (according to the New York Heart Association classification Class II to Class IV) (Dolgin and NYHA 1994), arrhythmias, bradycardia (resting pulse rate \<50 beats/minute), or hypotension (systolic and diastolic blood pressures \<100 and 60 millimeters of mercury (mmHg), respectively). * The participant has a history of cerebrovascular accident. * The participant has a known or suspected intolerance or hypersensitivity to the investigational product, PTH derivatives, or any of the stated ingredients.