The adoption of Artificial Intelligence (AI) in healthcare has improved diagnostic accuracy, particularly in medical imaging. However, the opaque nature of deep learning models raises concerns about interpretability in high-stakes applications such as pneumonia diagnosis. This study proposes an Explainable AI (XAI) framework that integrates a Hybrid CNN-ViT architecture with SHAP (SHapley Additive Explanations) for pneumonia detection from chest X-rays. Our approach achieves competitive diagnostic performance (94% accuracy) while enhancing transparency by highlighting clinically relevant features such as lobar consolidations and ground-glass opacities. By grounding explanations in established radiological findings, the framework supports clinical trust and regulatory compliance. This work contributes to bridging the gap between AI performance and medical accountability, positioning explainable deep learning as a trustworthy tool for real-world healthcare deployment.