The main purpose of this study is to evaluate a once daily (QD) 40-milligram (mg) oral dose of LY2940094 in participants with an alcohol dependency to evaluate if LY2940094 will reduce alcohol drinking in these participants. The study will last for 8 weeks.

Inclusion Criteria:

• Present with alcohol dependence (AD) defined by the Diagnostic and Statistical Manual of Mental Disorders, Fourth Edition, Text Revision (DSM-IV-TR 303.9)
• Must have 3 to 6 heavy drinking days per week as assessed by the Timeline Follow Back (TLFB) scale at screening and baseline (heavy drinking is defined as greater than 4 drinks per day for females and greater than 5 drinks per day for males)
• Have a body mass index (BMI) between 18 and 35 kilograms per square meter (kg/m^2)

Exclusion Criteria:

• Have had prior seizures or other condition that would place the participant at increased risk of seizures, and participants taking anticonvulsants for seizure control
• Have any other clinically significant medical condition or circumstance prior to randomization that, in the opinion of the investigator, could affect participant safety
• Meet Diagnostic and Statistical Manual of Mental Disorders, Fourth Edition, (DSM-IV) Axis I criteria for a lifetime diagnosis of schizophrenia, schizoaffective disorder, bipolar I disorder, or other psychoses