Total Thyroidectomy With and Without Prophylactic Central Neck Lymph Node Dissection in People With Low-risk Papillary Thyroid Cancer

* INCLUSION CRITERIA:
* Patients must have histologically or cytologically confirmed at least 1 thyroid nodule that is greater than or equal to1 cm. but less than or equal to 4 cm measured in greatest dimension and confirmed by the Laboratory of Pathology, National Cancer Institute (NCI) or confirmed by the pathology laboratory of the enrolling institution:

  * Indeterminate thyroid biopsy per Bethesda System for reporting thyroid cytopathology with B-Raf Proto-oncogene Serine/Threonine Kinase (BRAF) Valine 600 Glutamic Acid (V600E) mutation or rearranged in transformation/papillary thyroid carcinomas (RET/PTC) rearrangement
  * Cytologically or histologically suspicious or confirmed PTC per Bethesda System for reporting thyroid cytopathology.
* Age greater than or equal to 18 years. Because PTC occurs rarely in patients \<18 years of age, children are excluded from this study.
* Absence of radiographic evidence of extrathyroidal extension.
* Absence of abnormal lymphadenopathy suggesting metastatic PTC on physical examination and/or imaging studies.
* Eastern Cooperative Oncology Group (ECOG) performance status less than or equal to 2
* Patients must have adequate organ function to safely undergo general anesthesia and thyroidectomy. Laboratory values obtained less than or equal to 4 weeks prior to surgery must demonstrate adequate bone marrow function (hemoglobin (Hb) greater than or equal to 6.0 mmol/L, absolute neutrophil count greater than or equal to 1.5 x 10\^9/L, platelets greater than or equal to 80 x 10\^9/L), liver function (serum bilirubin less than or equal to 2 x upper limit of normal (ULN), serum transaminases less than or equal to 3 x ULN). Patients with chronic kidney disease who are on chronic renal replacement therapy are allowed. Other tests, such as pulmonary function tests, cardiac echocardiogram or stress test, will be performed if clinically indicated.
* Ability of subject to understand and the willingness to sign a written informed consent document.
* Women must not become pregnant prior to surgery or during the first 3 months after surgery. Women who can become pregnant will be asked to practice an effective form of birth control for up to 3 months after surgery.

EXCLUSION CRITERIA:

* Patients who have had previous thyroid surgery
* Patients whose tumors are deemed unresectable by clinical/imaging criteria.
* Patients with known synchronous distant metastatic disease.
* Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements.
* Pregnant women are excluded because we do not want to expose the unborn child to the procedures necessary to perform the surgery.