Inclusion Criteria:

- Histologically confirmed biliary tract carcinoma

- Surgically unresectable disease

- Meets any of the following criteria for biliary cancers only:

- Received ≤ 1 prior systemic anticancer therapy, including chemoembolization

- Received prior cryotherapy, radiofrequency ablation, ethanol injection,
transarterial chemoembolization, or photodynamic therapy AND meets the following
criteria:

- More than 6 weeks have elapsed since any of the prior therapy described
above

- Indicator lesion(s) must be outside the area of prior treatment OR must
demonstrate clear evidence of disease progression if the only indicator
lesion is inside the prior treatment area

- Indicator lesion must have clearly distinct edges on CT scan

- Prior radiotherapy with or without the use of a fluoropyrimidine as a
radiosensitizer is allowed, provided more than 12 weeks have elapsed since
treatment

- Fresh or paraffin-embedded tissue from tumor blocks must be available for review

- Measurable disease, defined as ≥ 1 unidimensionally measurable lesion > 20 mm by
conventional techniques or > 10 mm by spiral CT scan

- No known brain metastases

- Life expectancy > 12 weeks

- ECOG performance status (PS) 0-1 or Karnofsky PS 70-100%

- ANC ≥ 1,500/μL

- Platelet count ≥ 75,000/μL

- Total bilirubin ≤ 2 times upper limit of normal(ULN)

- AST or ALT ≤ 3 times ULN

- Serum albumin ≥ 2.5 mg/dL

- INR ≤ 1.5 (not receiving anticoagulation therapy)

- Creatinine normal or creatinine clearance ≥ 60 mL/min

- Not pregnant or nursing

- Negative pregnancy test

- Fertile women must use effective contraception during and for four weeks after the
last dose of AZD6244

- Fertile men must use effective contraception during and for 16 weeks after the last
dose of AZD6244

- No significant traumatic injury within the past 3 weeks

- No uncontrolled symptoms consistent with encephalopathy

- No history of allergic reactions attributed to compounds of similar chemical or
biologic composition to AZD6244 or its excipient, Captisol®

- No QTc interval > 500 msecs or other factors that increase the risk of QT
prolongation or arrhythmic events (e.g., hypokalemia or family history of long QT
interval syndrome), including NYHA class III-IV heart failure

- No other malignancy within the past 3 years, except adequately treated basal cell or
squamous cell skin cancer or carcinoma in situ of the cervix

- No refractory nausea and vomiting, chronic gastrointestinal disease (e.g.,
inflammatory bowel disease), or significant bowel resection that would preclude
adequate absorption

- No uncontrolled concurrent illness including, but not limited to, ongoing or active
infection or psychiatric illness/social situation that would limit compliance with
study requirements

- No malignant hypertension within the past year

- No prior sorafenib or MEK inhibitors

- More than 4 weeks since prior chemotherapy, biologic therapy, or immunotherapy (6
weeks for nitrosoureas or mitomycin C) and recovered to ≤ grade 1 adverse events

- No major surgery within the past 3 weeks

- No other concurrent investigational agents

- No concurrent requirement for medication that can prolong the QT interval

- No concurrent combination antiretroviral therapy for HIV-positive patients

- No concurrent consumption of grapefruit or grapefruit juice