Chronic diseases — including cardiovascular disease, diabetes mellitus, and chronic kidney disease (CKD) — represent the leading causes of global morbidity and mortality. Early, accurate, and interpretable prediction remains a critical clinical challenge. This study presents a systematic comparative analysis of five machine learning classifiers — Logistic Regression, Random Forest, Support Vector Machine (SVM), XGBoost, and LightGBM — across three benchmark datasets: the Cleveland Heart Disease dataset, the Pima Indians Diabetes dataset, and the UCI Chronic Kidney Disease dataset. Models are evaluated using Accuracy, Precision, Recall, F1-Score, and ROC-AUC under a unified preprocessing and evaluation framework. SHAP (SHapley Additive exPlanations) values are computed for LightGBM to provide clinically interpretable feature contributions. Results demonstrate that ensemble methods — particularly LightGBM and Random Forest — consistently outperform classical approaches. LightGBM achieves ROC-AUC of 0.9556, 0.8243, and 1.0000 on Heart Disease, Diabetes, and CKD respectively. SHAP analysis identifies ca, cp, and thal as dominant cardiac predictors; Glucose and BMI as primary diabetes biomarkers; and hemoglobin and specific gravity as near-perfect CKD discriminators — all consistent with established clinical literature. The high CKD separability (5-fold CV AUC = 0.9996 ± 0.0008) is confirmed as a genuine dataset property rather than overfitting. This work provides a reproducible, open-source benchmark for multi-disease ML prediction with explainability. Keywords: Machine Learning, Chronic Disease Prediction, Explainable AI, SHAP, XGBoost, LightGBM, Healthcare Informatics, Multi-Dataset Benchmark, Tabular Classification