BLASST-1 (Bladder Cancer Signal Seeking Trial): Nivolumab, Gemcitabine, and Cisplatin in Treatment of Muscle Invasive Bladder Cancer (MIBC) Undergoing Cystectomy

Inclusion Criteria: * Diagnosis of MIBC (predominantly urothelial carcinoma) with clinical stage T2-T4a and N\<1 disease (solitary lymph node measuring \< 2 cm) and M0 and deemed eligible for radical cystectomy. * Age ≥ 18 years * ECOG Performance Status of 0 or 1. * Required initial laboratory values within 14 days of study enrollment: * Absolute Neutrophil Count ≥ 1500 cells/mm\^3 * Platelets ≥ 100,000 cells/mm\^3 * Hemoglobin ≥ 9.0 g/dL * Bilirubin ≤ 1.5 times the upper limit of normal (ULN) for the institution (For patients with known Gilbert's disease: bilirubin ≤ 3 x ULN) * Aspartate transaminase (AST) and alanine transaminase (ALT) ≤ 3.0 x ULN for the institution * Creatinine clearance ≥ 50 ml/min by Cockcroft-Gault formula or 24 hour urinary clearance (CrCl = \[140-age (years)\] x actual weight (kg) / \[72 x serum Cr (mg/dL)\] (if patient is female multiply the above by 0.85) or 24 hour urinary creatinine clearance. * Alkaline phosphatase ≤ 2.5 x ULN for the institution * INR and aPTT ≤ 1.5 x ULN if not on therapeutic anticoagulation. Patients receiving therapeutic anticoagulation will be allowed if maintained on a stable dose. * Females of childbearing potential and males who are not surgically sterile and with partners of childbearing potential must agree to use effective contraception during study treatment for 5 months for females and 7 months for males after the last dose of nivolumab. * Ability to provide a signed and dated consent or have a legally authorized representative to provide written and signed consent prior to the initiation of any research related procedures. * Patient must agree to submission of archived tumor (20-25 formalin-fixed paraffin embedded (FFPE) slides of 5-10 microns in thickness) from TURBT and radical cystectomy tissues. If archived samples are not available fresh tissue will be used. * Ability to provide written consent prior to the initiation of any research related procedures. Exclusion Criteria: * Presence of N2-3 or M1 disease. * Ineligible to receive cisplatin by meeting one or more of the following criteria; * Creatinine clearance of \< 50 mL/min * Hearing loss of 25 dB at two contiguous frequencies with testing required if a patient has hearing loss - At the investigator's discretion, and after discussion with the patient, this exclusion may be waived if the potential benefit of cisplatin therapy is felt to outweigh the risk of further hearing loss. * CTCAE v4 Grade 2 or higher peripheral neuropathy, * New York Heart Association Class III or IV heart failure * ECOG performance status 2 or higher. * Prior systemic therapy (intravenous) is not permitted. Prior intravesical therapies including intravesical gemcitabine is permitted for non-muscle invasive disease (i.e. T1 or lower). * Prior treatment with cisplatin for bladder cancer. * Prior treatment with anti-PD-1, CTLA-4, or anti-PD-L1 therapeutic antibody or pathway-targeting agents. * Prior therapeutic radiation to the bladder. * Major surgical procedure within 28 days prior to Cycle 1, Day 1 or anticipation of need for a major surgical procedure during the course of the study. * Any of the following within the 6 months prior to study drug administration: myocardial infarction, severe/unstable angina, symptomatic congestive heart failure (\>New York Heart Association Class 2), stroke, serious cardiac arrhythmia. * Human immunodeficiency virus (HIV) infection or acquired immunodeficiency syndrome (AIDS)-related illness. * Pregnancy, lactation, or breast-feeding. Women of childbearing potential must have a negative urine pregnancy test at screening. * History of autoimmune disease, including but not limited to myasthenia gravis, myositis, autoimmune hepatitis, systemic lupus erythematosus, rheumatoid arthritis, inflammatory bowel disease, Wegener's granulomatosis, vascular thrombosis associated with antiphospholipid syndrome, Sjogren's syndrome, Guillain-Barre syndrome, multiple sclerosis, systemic vasculitis, or glomerulonephritis. * History of idiopathic pulmonary fibrosis, pneumonitis (including drug induced), organizing pneumonia (i.e., bronchiolitis obliterans, cryptogenic organizing pneumonia, etc.), or evidence of active pneumonitis on screening chest computed tomography (CT) scan, history of radiation pneumonitis in the radiation field (fibrosis) is permitted. * Active hepatitis B virus (HBV, chronic or acute, defined as having a positive hepatitis B surface antigen \[HBsAg\] test at screening) or hepatitis C antibody. Patients with past HBV infection or resolved HBV infection (defined as the presence of hepatitis B core antibody \[HBc Ab\] and absence of HBsAg) are eligible. HBV DNA must be obtained in these patients prior to Cycle 1, Day 1 and confirmed to be negative. Patients positive for hepatitis C virus (HCV) antibody are eligible only if polymerase chain reaction is negative for HCV RNA. * Active tuberculosis or BCG infection * Active infection requiring systemic antibiotics for more than 7 days within 3 days prior to Cycle 1, Day 1. Prophylactic short-term antibiotics will be allowed. * Administration of intravesical bacillus Calmette-Guerin (BCG) within 4 weeks before Cycle 1, Day 1 * Administration of a live, attenuated vaccine within 4 weeks before Cycle 1, Day 1 or anticipation that such a live attenuated vaccine will be required during the study. * Persisting toxicity from prior therapy (NCI CTCAE v4.03 Grade \>1); however alopecia or other Grade \<2 AEs not constituting a safety risk, based on Investigator's judgement, are acceptable. * History of or active bone marrow disorders expected to interfere with study therapy (e.g. acute leukemias, accelerated/blast-phase chronic myelogenous leukemia, chronic lymphocytic leukemia, Burkitt lymphoma, plasma cell leukemia, or non-secretory myeloma). * Prior allogeneic stem cell or solid organ transplant. * Known primary central nervous system (CNS) malignancy. * Patients with eczema, psoriasis, lichen simplex chronicus of vitiligo with dermatologic manifestations only (e.g., patients with psoriatic arthritis would be excluded) are permitted but patients with psoriasis require a baseline ophthalmologic exam to rule out ocular manifestations. Rash must cover less than 10% of body surface area (BSA) and must be well controlled at baseline and only requiring topical steroids. * Any other chronic medical condition or psychiatric condition, physical examination finding, or clinical laboratory finding giving reasonable suspicion of a disease or condition that contraindicates the use of an investigational drug or that may affect the interpretation of the results or render the patient at high risk from treatment complications * Known additional malignancy that is progressing or requires active treatment. Exceptions include basal cell carcinoma of the skin, squamous cell carcinoma of the skin or in situ cervical cancer that has undergone potentially curative therapy. Patients on androgen deprivation therapy as part of adjuvant therapy after radiation for prostate cancer or patients on adjuvant hormonal therapies for breast cancer will be allowed if they are being considered for curative intent for bladder cancer. * Treatment with systemic immunostimulatory agents (including but not limited to interferon \[IFN\]-a or interleukin \[IL\]-2) within 4 weeks or five half-lives of the drug (whichever is shorter) prior to Cycle 1, Day 1 * Concomitant use of systemic corticosteroids at physiologic doses or \<10 mg/day of prednisone or equivalent. * Concomitant use of another investigational agent and/or treatment with an investigational agent within 4 weeks prior to Cycle 1, Day 1 (or within five halflives of the investigational product, whichever is longer). * Use of bisphosphonate therapy for osteoporosis will be allowed if started prior to study enrollment.