A thick connective tissue capsule separates the glands from the thyroid tissue. Most people have four parathyroid glands, but occasionally there are more in tissues of the neck or chest. The function of one type of parathyroid cells, the oxyphil cells, is not clear. The primary functional cells of the parathyroid glands are the chief cells. These epithelial cells produce and secrete the parathyroid hormone (PTH), the major hormone involved in the regulation of blood calcium levels. Parathyroid Glands The small parathyroid glands are embedded in the posterior surface of the thyroid gland.