This study will be a randomized, placebo-controlled pilot study to evaluate the effect of transdermal nicotine to 1) reduce subjective complaints and 2) enhance cognitive performance on laboratory measures of cognitive performance in breast cancer patients with persistent chemotherapy-related cognitive impairment (CRCI), a condition also known as "chemo brain." Participants will be randomized to either placebo or active compound (50/50) for the 6-week treatment portion of the study. Participants will be assessed before, during, and at the end of treatment. At the end of the 8-week study, participants will have the option to take part in the open-label portion of the study for an additional 6 weeks.