**Core Concept**
Anaplastic carcinoma of the thyroid is a highly aggressive and rare form of thyroid cancer characterized by rapid growth and infiltration into surrounding tissues. The treatment of choice for anaplastic carcinoma of the thyroid involves a multidisciplinary approach, including surgery, radiation therapy, and chemotherapy, with the goal of improving survival and quality of life.

**Why the Correct Answer is Right**
The correct answer involves a combination of external beam radiation therapy (EBRT) and chemotherapy, as these modalities have been shown to improve local control and survival in patients with anaplastic thyroid carcinoma. **EBRT** can help control the growth of the tumor, while chemotherapy can target the rapidly dividing cancer cells. In the case of a tumor infiltrating the sternum, a combination of EBRT and chemotherapy is often considered the most effective treatment option.

**Why Each Wrong Option is Incorrect**
**Option A:** Surgery alone is generally not recommended for anaplastic thyroid carcinoma due to its aggressive nature and tendency to infiltrate surrounding tissues.
**Option B:** Targeted therapy may be considered for some patients with anaplastic thyroid carcinoma, but it is not the treatment of choice for a tumor infiltrating the sternum.
**Option C:** Palliative care is an important aspect of managing anaplastic thyroid carcinoma, but it is not the primary treatment for a tumor infiltrating the sternum.

**Clinical Pearl / High-Yield Fact**
For patients with anaplastic thyroid carcinoma, a multidisciplinary treatment approach, including a medical oncologist, radiation oncologist, and surgeon, is essential for optimal management.

**Correct Answer:** C.