Reframing a negative into a positive thought is at the crux of several cognitive approaches to mental health and psychotherapy that could be made more accessible by large language model-based solutions. Such reframing is typically non-trivial and requires multiple rationalization steps to uncover the underlying issue of a negative thought and transform it to be more positive. However, this rationalization process is currently neglected by both datasets and models which reframe thoughts in one step. In this work, we address this gap by augmenting open-source datasets for positive text rewriting with synthetically-generated Socratic rationales using a novel framework called SOCRATICREFRAME. SOCRATICREFRAME uses a sequence of question-answer pairs to rationalize the thought rewriting process. We show that such Socratic rationales significantly improve positive text rewriting for different open-source LLMs according to both automatic and human evaluations guided by criteria from psychotherapy research. We validate our framework and the synthetic rationalizations with expert judgements from domain experts and psychology students in an IRB-approved annotation study. Our findings highlight the potential of utilizing the synergy between LLM reasoning and established psychotherapy techniques to build assistive solutions for reframing negative thoughts.