The overall goal of the present project is to investigate whether lisdexamphetamine (LDX; Vyvanse) is an effective adjunct to nicotine replacement therapy (NRT) to promote smoking cessation in patients with comorbid Attention Deficit Hyperactivity Disorder (ADHD) and nicotine dependence. The investigators hypothesized initially that smokers with ADHD who are optimized to a dose of LDX prior to quitting smoking and who remain on this dose of medication after quitting will remain abstinent longer than patients who are treated with placebo before and after quitting.However due to recent key issues that have arisen showing that initiation of stimulant treatment while subjects are actively smoking may facilitate increased smoking, and given that the study was still in the very early stage of study execution, the investigators revised the study design to use an empirically validated pretreatment approach with NRT and to initiate LDX treatment on the first post quit date in order to reduce the withdrawal symptoms that accompany smoking cessation. The overall rationale for this revised study design remains similar to the original.