Inclusion Criteria:

          -  Pathologically (histologically or cytologically) proven diagnosis of anaplastic
             thyroid cancer (a diagnosis that is noted to be consistent with anaplastic thyroid
             cancer is acceptable).

          -  Metastatic disease or local-regional disease that is considered not resectable for
             cure.

          -  Patients must have measurable disease per RECIST v1.1 criteria, defined as at least
             one lesion that can be accurately measured in at least one dimension (longest diameter
             to be recorded for non-nodal lesions and short axis for nodal lesions) as ≥20 mm with
             conventional techniques or as ≥10 mm with spiral CT scan, MRI, or calipers by clinical
             exam

          -  Age ≥18 years

          -  ECOG performance status ≤2 (or Karnofsky ≥60)

          -  Able to swallow and retain orally-administered medication and does not have any
             clinically significant gastrointestinal abnormalities that may alter absorption, such
             as malabsorption syndrome or major resection of the stomach or bowels

          -  No CTCAE v4 grade >2 neuropathy

          -  Patients must have normal organ and marrow function as defined below:

               -  Absolute neutrophil count (ANC) ≥1.5x10^9/L

               -  Hemoglobin ≥9 g/dL

               -  Platelets ≥100x10^9/L

               -  Serum bilirubin ≤1.5x institutional upper limit of normal (ULN) (Unless Gilbert's
                  Disease in which case total bilirubin ≤3x institutional ULN)

               -  Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) ≤2.5x
                  institutional ULN (≤5x institutional ULN if there is liver metastasis)

               -  Serum creatinine ≤1.5 mg/dL OR calculated creatinine clearance (Cockcroft-Gault
                  formula) ≥50 mL/min OR 24-hour urine creatinine clearance ≥50 mL/min

               -  Left ventricular ejection fraction ≥ institutional lower limit of normal (LLN) by
                  ECHO or MUGA

          -  Negative pregnancy test (serum or urine) within 14 days of registration in women of
             child-bearing potential. Women of child-bearing potential and men must agree to use
             adequate contraception (hormonal or barrier method of birth control; abstinence) prior
             to study entry and for the duration of study participation. Men treated or enrolled on
             this protocol must also agree to use adequate contraception prior to the study, for
             the duration of study participation, and 4 months after completion of trametinib
             administration

          -  Ability to understand and the willingness to sign a written informed consent document.

        Exclusion Criteria:

          -  Patients who have had chemotherapy or radiotherapy within 7 days of starting
             treatment.

          -  Symptomatic or untreated brain metastases, leptomeningeal disease, or spinal cord
             compression

          -  History of interstitial lung disease or pneumonitis

          -  History or current evidence/risk of retinal vein occlusion (RVO) or central serous
             retinopathy (CSR):

               -  History of RVO or CSR, or predisposing factors to RVO or CSR (e.g., uncontrolled
                  glaucoma or ocular hypertension)

               -  Visible retinal pathology as assessed by ophthalmic exam that is considered a
                  high risk factor for RVO or CSR such as evidence of new optic disc cupping,
                  evidence of new visual field defects, and intraocular pressure >21 mm Hg

          -  History or evidence of cardiovascular risk including any of the following:

               -  LVEF<LLN

               -  A QT interval corrected for heart rate using the Bazett's formula QTcB ≥480 msec

               -  History or evidence of current clinically significant uncontrolled arrhythmias
                  (exception: patients with controlled atrial fibrillation for >30 days prior to
                  -enrollment are eligible)

               -  History of acute coronary syndromes (including myocardial infarction and unstable
                  angina), coronary angioplasty, or stenting within 6 months prior to randomization

               -  History or evidence of current ≥ Class II congestive heart failure as defined by
                  the New York Heart Association (NYHA) functional classification system

               -  Treatment-refractory hypertension defined as a blood pressure of systolic >150
                  mmHg and/or diastolic >90 mmHg which cannot be controlled by anti-hypertensive
                  therapy

               -  Known cardiac metastases

          -  Known Human Immunodeficiency Virus (HIV), Hepatitis B Virus (HBV), or Hepatitis C
             Virus (HCV) infection (with the exception of chronic or cleared HBV and HCV infection,
             which will be allowed) HIV-positive patients on combination antiretroviral therapy are
             ineligible because of the potential for pharmacokinetic interactions with trametinib.
             In addition, these patients are at increased risk of lethal infections when treated
             with marrow-suppressive therapy. Appropriate studies will be undertaken in patients
             receiving combination antiretroviral therapy when indicated

          -  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

          -  Any condition that may impair the ability to absorb oral medications/investigational
             product including: prior surgical procedures affecting absorption including, but not
             limited to major resection of stomach or small bowel; active peptic ulcer disease; and
             malabsorption syndrome

          -  Any major surgery within 21 days prior to enrollment.

          -  Have a known immediate or delayed hypersensitivity reaction or idiosyncrasy to taxanes
             and drugs chemically related to trametinib, or excipients or to dimethyl sulfoxide
             (DMSO)

          -  Current use of a prohibited medication. The following medications or non-drug
             therapies are prohibited:

               -  Concurrent treatment with bisphosphonates is permitted; however, treatment must
                  be initiated prior to the first dose of study therapy. Prophylactic use of
                  bisphosphonates in patients without bone disease is not permitted, except for the
                  treatment of osteoporosis

               -  Because the composition, PK, and metabolism of many herbal supplements are
                  unknown, the concurrent use of all herbal supplements is prohibited during the
                  study (including, but not limited to, St. John's wort, kava, ephedra [ma huang],
                  gingko biloba, dehydroepiandrosterone [DHEA], yohimbe, saw palmetto, or ginseng)