Inclusion Criteria:  between 18 and 60 years of age. meet DSM-5 criteria for current cocaine use disorder as measured by the Structured Clinical Interview for DSM-5 (SCID). have at least 1 cocaine-positive urine specimen (≥ 150 ng/mL) during intake. be in acceptable health on the basis of interview, medical history and physical exam. have hematology and chemistry laboratory tests that are within reference limits (±10%), with the following exception: pancreatic tests (lipase and amylase) must be within normal limits. consent to use an acceptable method of birth control during study participation and for one month after discontinuation of the study medication. Non-hormonal methods of contraception are recommended, including barrier contraceptives (e.g., diaphragm, cervical cap, male condom) or intrauterine device (IUD). Steroid contraceptives if used with non-hormonal methods are acceptable. be able to understand the consent form and provide written informed consent. be able to provide the names of at least 2 persons who can generally locate their whereabouts.  Exclusion Criteria:  current DSM-5 diagnosis for substance use disorder (of at least moderate severity) other than cocaine, marijuana, alcohol, or nicotine. current alcohol use that meets for physiological dependence requiring detoxification or makes participation medically unsafe as determined by the medical director. have a DSM-5 axis I psychiatric disorder, or anorexia nervosa, or neurological disease or disorder requiring ongoing treatment and/or making study participation unsafe (e.g., psychosis, dementia). significant current suicidal or homicidal ideation. Type 1 or type 2 diabetes mellitus (previously diagnosed or indicated by HbA1C level of ≥6.5%). have medical conditions contraindicating exenatide pharmacotherapy (e.g., personal or family history of medullary thyroid carcinoma or multiple endocrine neoplasia syndrome type 2, severe gastrointestinal disease (severe gastroparesis), previous history of pancreatitis or risk of pancreatitis, creatinine clearance <45 or end stage renal disease, previous medically adverse reaction to exenatide or other GLP-1 receptor agonists). taking medications that could adversely interact with exenatide (e.g., oral or injectable blood glucose lowering medications). having conditions of probation or parole requiring reports of drug use to officers of the court. impending incarceration. pregnant or nursing for female patients.