The goal of this study is to investigate peanut sublingual immunotherapy (SLIT) as a treatment for children with peanut allergy. This study is primarily designed to evaluate the efficacy and safety of peanut SLIT compared to placebo after 12 months. Secondarily, the study is designed to evaluate the efficacy of extended maintenance dosing of peanut SLIT in inducing lasting tolerance after discontinuation of the peanut SLIT. Mechanistic studies will be completed concurrently as exploratory endpoints to understand changes in the allergic immune response related to peanut SLIT.