Inclusion Criteria:

1. Age ≥ 1 year
2. Histologic diagnosis of a differentiated thyroid cancer, s/p thyroidectomy and adequate local therapy (e.g., lymph node dissection as per standard of care) for metastatic disease in the neck in the opinion of the treating investigator
3. Anatomically evaluable disease on chest CT meeting one of the following criteria (obtained within 90 days of enrollment):

A. multiple (\> 10) noncalcified solid pulmonary nodules visible on CT and/or

B. enlarging, discrete pulmonary nodules visible on CT of any number consistent with metastatic disease
4. Identification of an neurotrophic tyrosine receptor kinase (NTRK) (NTRK1, NTRK2, or NTRK3) gene fusion in a CLIA/CAP accredited laboratory without known kinase domain resistance mutation
5. Lansky/Karnofsky performance status ≥ 50%
6. Adequate Organ Function

A. Bone Marrow Function:
* Peripheral absolute neutrophil count (ANC) ≥ 1000/mm3
* Platelet count ≥ 100,000/mm3 (transfusion independent, defined as not receiving platelet transfusions for at least 7 days prior to enrollment)
* Hemoglobin ≥ to 8.0 g/dL at baseline (may receive red blood cell (RBC) transfusions).

B. Adequate Renal Function:

Creatinine clearance or radioisotope glomerular filtration rate (GFR) ≥ 70 mL/min/1.73 m2 or a maximum serum creatinine based on age/gender as follows:

Age Maximum Serum Creatinine (mg/dL) Male Female 1 to \< 2 years 0.6 0.6 2 to \< 6 years 0.8 0.8 6 to \< 10 years 1 1 10 to \< 13 years 1.2 1.2 13 to \< 16 years 1.5 1.5

≥ 16 years 1.7 1.7

C. Adequate Liver Function
* Bilirubin (sum of conjugated + unconjugated) ≤ 1.5 x upper limit of normal (ULN) for age.
* Serum glutamic-pyruvic transaminase (SGPT) (ALT) ≤ 135 U/L. For the purpose of this study, the ULN for SGPT is 45 U/L.
* Serum albumin ≥ 2 g/dL
7. Female patients of reproductive potential must agree to use a highly effective contraceptive method for the duration of study therapy and for at least one month after the final dose of larotrectinib. Males of reproductive potential with a non-pregnant female partner of child-bearing potential must use a highly effective contraception for the duration of the study and for at least one month after the final dose of larotrectinib.

Exclusion Criteria

1. No prior systemic therapy for thyroid cancer, including tropomyosin receptor kinase (TRK) inhibitors or 131I.
2. Females who are pregnant or breastfeeding are excluded due to the potential risks of larotrectinib and RAI to the fetus/neonate.
3. Concurrent therapy: Patients currently receiving a strong CYP3A4 inducer or inhibitor are not eligible. Strong inducers or inhibitors of CYP3A4 should be avoided 14 days prior to treatment to the end of the study treatment.