The advent of personalized medicine, or precision medicine, promises a revolution in healthcare, offering treatments tailor-made to the genetic makeup and lifestyle choices of individuals. Despite the significant potential, its integration into mainstream healthcare is hindered by several challenges, including data silos, privacy concerns, and a lack of coordinated efforts across the healthcare ecosystem. This paper examines the role of Blockchain technology as a solution to these obstacles. By leveraging the unique attributes of Blockchain we propose a model for a healthcare system that aligns with the ideals of personalized medicine. Through conceptual analysis and discussing initiatives like the 100,000 Genomes Project, we illustrate the synergy between Blockchain and personalized medicine. The paper concludes by envisioning an integrated healthcare delivery model that not only advances drug research and treatments but also significantly improves patient outcomes through personalized care approaches.