This is a pilot study examining the efficacy, safety and tolerability of intranasal oxytocin as a novel treatment in Phelan-McDermid syndrome (PMS). This study will utilize a randomized, placebo-controlled design for 12 weeks (phase 1), followed by an open-label extension for 12 weeks (phase 2). The purpose is to evaluate the effect of intranasal oxytocin on impairments in attention, social memory, socialization, language, and repetitive behaviors.