**Core Concept**
Medullary thyroid carcinoma (MTC) is a type of thyroid cancer that originates from the parafollicular cells, also known as C-cells. These cells are responsible for producing calcitonin, a hormone involved in calcium homeostasis. In MTC, the abnormal C-cells lead to the excessive production of calcitonin, which can serve as a tumor marker.

**Why the Correct Answer is Right**
The correct answer is calcitonin because it is a hormone produced by the parafollicular cells of the thyroid gland. Elevated levels of calcitonin are associated with medullary thyroid carcinoma, making it a useful tumor marker for diagnosis and monitoring of the disease. Calcitonin is measured in the blood and can be used to detect recurrence or metastasis of MTC.

**Why Each Wrong Option is Incorrect**
**Option A:** Carcinoembryonic antigen (CEA) is a tumor marker for various cancers, including colorectal, breast, and lung cancers, but it is not specific to medullary thyroid carcinoma.

**Option B:** Thyroglobulin is a protein produced by thyroid follicular cells and is often used as a tumor marker for papillary and follicular thyroid cancers, but not for medullary thyroid carcinoma.

**Option C:** Procalcitonin is a precursor to calcitonin and is elevated in various conditions, including sepsis and pneumonia, but it is not specific to medullary thyroid carcinoma.

**Clinical Pearl / High-Yield Fact**
It's essential to remember that calcitonin is a specific tumor marker for medullary thyroid carcinoma, and its measurement can aid in the diagnosis and monitoring of this disease.

**Correct Answer:** C. Calcitonin.