This is a phase II study (the second stage of testing a new drug or new drug combinations) to see how useful two different schedules of study drug selumetinib with cisplatin and gemcitabine are compared to cisplatin and gemticabine alone in patients with biliary cancer.

Selumetinib, an oral drug which plays an important role in the regulation of cell growth (MEK 1/2 inhibitor) has been shown to shrink tumours in patients with biliary cancer and other types of human cancers. Selumetinib has also been shown to shrink tumours when given in combination with cisplatin and gemcitabine in research studies done in animals and in some patients with biliary tract cancer. Cisplatin and gemcitabine are intravenous drugs that work by damaging DNA in tumor cells so that they are unable to grow and divide.

Inclusion Criteria:

• Unresectable, recurrent or metastatic, measurable biliary tract cancer or gall bladder cancer
• No prior systemic therapy
• Performance status 0, 1, or 2
• Age 18 years or older
• Estimated life expectancy > 3 months
• Adequate hematological, liver, renal function
• No evidence of active uncontrolled infection
• Capable of giving written consent
• Acceptable recovery of previous side effects

Exclusion Criteria:

• Progressing within 3 or 6 months of receiving certain treatments
• Prior chemotherapy for non-resectable or metastatic disease or a MEK inhibitor
• Progressing within 6 months of adjuvant treatment.
• May not have received prior chemotherapy for non-resectable/metastatic disease.
• Prior MEK, RAS, or RAF inhibitors or history of hypersensitivity to study drugs.
• Ampullary carcinoma
• Incomplete recovery from previous surgery
• Undergoing treatment with curative intent
• Prior malignancy that could interfere with the response evaluation
• Severe or uncontrolled systemic diseases or lab finding that makes it undesirable for patient to participate
• Any psychiatric or other disorder likely to impact consent
• Pregnant or breastfeeding
• Patients with significant cardiac-related issues
• History of eye-related issues.
• Systemic disease, active infection, bleeding diatheses or renal transplant, including hep B, hep C or HIV
• Receiving potent inhibitors or inducers of CYP3A4/5, CYP2C19 and CYP1A2 can continue with caution