Traditional recommender systems (RS) have been primarily optimized for accuracy and short-term engagement, often overlooking transparency and trustworthiness. Recently, platforms such as Amazon and Instagram have begun providing recommendation rationales to users, acknowledging their critical role in fostering trust and enhancing engagement; however, most existing systems still treat them as post-hoc artifacts. We propose an LLM-based recommender (LLM-Rec) that not only predicts items but also generates logically grounded rationales. Our approach leverages a self-annotated rationale dataset and instruction tuning in a rationale-first format, where the model generates an explanation before outputting the recommended item. By adopting this strategy and representing rationales in a chain-of-thought (CoT) style, LLM-Rec strengthens both interpretability and recommendation performance. Experiments on the Fashion and Scientific domains of the Amazon Review dataset demonstrate significant improvements over well-established baselines. To encourage reproducibility and future research, we publicly release a rationale-augmented recommendation dataset containing user histories, rationales, and recommended items.