**Core Concept**
Medullary carcinoma of the thyroid (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 that helps regulate calcium levels in the blood.

**Why the Correct Answer is Right**
The tumor marker for medullary carcinoma of the thyroid is calcitonin. Elevated levels of calcitonin in the blood are a diagnostic indicator of MTC. This is because MTC cells produce and secrete calcitonin in large quantities, leading to a significant increase in serum calcitonin levels. Calcitonin is secreted by the C-cells of the thyroid gland, which are the cells from which MTC originates.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because TSH (Thyroid-Stimulating Hormone) is a marker for thyroid function, not a specific marker for medullary carcinoma.

**Option B:** This option is incorrect because CEA (Carcinoembryonic Antigen) is a marker for several types of cancer, including colorectal, lung, and breast cancer, but it is not specific for medullary carcinoma of the thyroid.

**Option C:** This option is incorrect because Procalcitonin is a precursor to calcitonin and is elevated in conditions of bacterial infection and sepsis, but it is not a specific marker for medullary carcinoma.

**Clinical Pearl / High-Yield Fact**
Remember that calcitonin is a specific marker for medullary carcinoma of the thyroid and should be elevated in the serum of patients with this condition. It is essential to consider calcitonin levels in the differential diagnosis of thyroid nodules and masses.

**Correct Answer:** C. Calcitonin.