The evolution of wireless communication systems will be fundamentally impacted by an open radio access network (O-RAN), a new concept defining an intelligent architecture with enhanced flexibility, openness, and the ability to slice services more efficiently. For all its promises, and like any technological advancement, O-RAN is not without risks that need to be carefully assessed and properly addressed to accelerate its wide adoption in future mobile networks. In this paper, we present an in-depth security analysis of the O-RAN architecture, discussing the potential threats that may arise in the different O-RAN architecture layers and their impact on the Confidentiality, Integrity, and Availability (CIA) triad. We also promote the potential of zero trust, Moving Target Defense (MTD), blockchain, and large language models(LLM) technologies in fortifying O-RAN's security posture. Furthermore, we numerically demonstrate the effectiveness of MTD in empowering robust deep reinforcement learning methods for dynamic network slice admission control in the O-RAN architecture. Moreover, we examine the effect of explainable AI (XAI) based on LLMs in securing the system.