ADHD is a neurologic disorder that is thought to be caused by chemical imbalances of certain neurotransmitters in the brain. The disorder can cause inattention, hyperactivity, and impulsivity. Cocaine abuse rates in adults with ADHD are significantly higher than they are in adults who do not have the disorder. This may be reflective of an attempt by individuals with ADHD to self-treat symptoms. Atomoxetine is an FDA-approved drug that is used to increase the ability to pay attention and decrease impulsiveness and hyperactivity in children and adults with ADHD. The drug is in a class of medications called selective norepinephrine reuptake inhibitors and works by increasing the levels of norepinephrine, a natural substance in the brain that affects a person's attention and impulsivity. It is possible that reducing ADHD symptoms in cocaine abusers with ADHD will help decrease their need for cocaine. This study will evaluate the effectiveness of atomoxetine in reducing cocaine use in people with ADHD who abuse cocaine.