Large language models (LMs) beyond a certain scale, demonstrate the emergent capability of generating free-text rationales for their predictions via chain-of-thought (CoT) prompting. While CoT can yield dramatically improved performance, such gains are only observed for sufficiently large LMs. Even more concerning, there is little guarantee that the generated rationales are consistent with LM's predictions or faithfully justify the decisions. In this work, we propose a faithful knowledge distillation method to learn a small, self-consistent CoT model from a teacher model that is orders of magnitude larger. To form better supervision, we elicit rationales supporting the gold answers from a large LM (teacher) by contrastive decoding, which encourages the teacher to generate tokens that become more plausible only when the answer is considered. To ensure faithful distillation, we use the teacher-generated rationales to learn a student LM with a counterfactual reasoning objective, which prevents the student from ignoring the rationales to make inconsistent predictions. Experiments show that, while yielding comparable end-task performance, our method can generate CoT rationales that are more faithful than baselines do. Further analysis suggests that such a model respects the rationales more when making decisions; thus, we can improve its performance more by refining its rationales.