Pembrolizumab (MK3475), Gemcitabine, and Concurrent Hypofractionated Radiation Therapy for Muscle-Invasive Urothelial Cancer of the Bladder

Inclusion Criteria: * Histologically confirmed muscle-invasive urothelial cancer of the bladder within 60 days of study enrollment. Patients must be willing to provide a TURBT specimen during screening and prior to enrollment if adequate specimen (FFPE tissue block or 20 unstained slides) from initial TURBT documenting muscle-invasive urothelial bladder cancer is not available. * Clinical stage T2-T4a, N0, M0 urothelial bladder cancer. * Deemed to not be a candidate for radical cystectomy by attending urologic oncologist or refuse radical cystectomy. * Be willing and able to provide written informed consent/assent for the trial. * Be ≥ 18 years of age on day of signing informed consent. * Have a performance status of 0 or 1 on the Eastern Cooperative Oncology Group Performance Scale. * Demonstrate adequate organ function as defined below, all screening labs should be performed within 10 days of protocol enrollment. * Absolute neutrophil count \>= 1,500 /mcL; * Platelets \>= 100,000 /mcL; * Hemoglobin \>= 9.0 g/dL; * Serum creatinine \<=1.5 x upper limit of normal (ULN) or calculated creatinine clearance \>= 30 mL/min as calculated by Cockcrof-Gault formaulae or by 24 hour urine collection; * Serum total bilirubin \<=1.5 x ULN or direct bilirubin \<= ULN for subjects with total bilirubin levels \> 1.5 x ULN; * Aspartate aminotransferase and alanine aminotransferase \<= 1.5 x ULN; * Albumin \>= 2.5 mg/dL; * International normalized ratio or prothrombin time (PT) \<= 1.5 x ULN unless subject is receiving anticoagulant therapy as long as PT or partial prothrombin time (PTT) is within therapeutic range of intended use of anticoagulants; * Activated Partial Thromboplastin Time (aPTT) \<= 1.5 x ULN unless subject is receiving anticoagulant therapy as long as PT or PTT is within therapeutic range of intended use of anticoagulants. * Female subject of childbearing potential should have a negative urine or serum pregnancy within 72 hours prior to receiving the first dose of study medication. If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required. * Female subjects of childbearing potential should be willing to use 2 methods of birth control or be surgically sterile, or abstain from heterosexual activity for the course of the study through 120 days after the last dose of study medication. Subjects of childbearing potential are those who have not been surgically sterilized or have not been free from menses for \> 1 year. * Male subjects should agree to use an adequate method of contraception starting with the first dose of study therapy through 120 days after the last dose of study therapy. Exclusion Criteria: * Has received prior targeted small molecule therapy, radiation therapy or systemic chemotherapy for urothelial bladder cancer including neoadjuvant chemotherapy. Prior intravesical chemotherapy or intravesical immunotherapy is permissible, however, no prior intravesical therapy is permitted within 4 weeks of study enrollment; adjuvant therapy is not permitted. * Has received prior pelvic radiation therapy. * Has a history of inflammatory bowel disease or history of scleroderma. * Is currently participating and receiving study therapy or has participated in a study of an investigational agent and received study therapy or used an investigational device within 4 weeks of the first dose of treatment. * Has a diagnosis of immunodeficiency or is receiving systemic steroid therapy or any other form of immunosuppressive therapy within 7 days prior to the first dose of trial treatment. * Has a known history of active TB (Bacillus Tuberculosis). * Hypersensitivity to pembrolizumab or any of its excipients. * Has had a prior anti-cancer monoclonal antibody (mAb) within 4 weeks prior to study Day 1 or who has not recovered (i.e., ≤ Grade 1 or at baseline) from adverse events due to agents administered more than 4 weeks earlier. * If subject received major surgery, they must have recovered adequately from the toxicity and/or complications from the intervention prior to starting therapy. * Any prior history of invasive malignancy within the past 5 years except non-melanoma skin cancer, carcinoma in-situ, localized prostate cancer without biochemical recurrence following definitive treatment. * Has any history of inflammatory bowel disease or scleroderma. * Has other active autoimmune disease that has required systemic treatment in the past 2 years (i.e. with use of disease modifying agents, corticosteroids or immunosuppressive drugs). Replacement therapy (eg., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment. * History of Guillain-Barre Syndrome or Stevens-Johnson Syndrome * Has known history of, or any evidence of active, non-infectious pneumonitis. * Has an active infection requiring systemic therapy. * Has a history or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the trial, interfere with the subject's participation for the full duration of the trial, or is not in the best interest of the subject to participate, in the opinion of the treating investigator. * Has known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial. * Is pregnant or breastfeeding, or expecting to conceive or father children within the projected duration of the trial, starting with the pre-screening or screening visit through 120 days after the last dose of trial treatment. * Has received prior therapy with an anti-PD-1, anti-PD-L1, or anti-PD-L2 agent. * Has a known history of Human Immunodeficiency Virus (HIV) (HIV 1/2 antibodies). * Has known active Hepatitis B (e.g., HBsAg reactive) or Hepatitis C (e.g., HCV RNA \[qualitative\] is detected). * Has received a live vaccine within 30 days of planned start of study therapy. Seasonal influenza vaccines for injection are generally inactivated flu vaccines and are allowed; however intranasal influenza vaccines (e.g., Flu-Mist®) are live attenuated vaccines, and are not allowed.