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Chance imbalance in baseline characteristics is common in randomized clinical trials. Regression adjustment such as the analysis of covariance (ANCOVA) is often used to account for imbalance and increase precision of the treatment effect estimate. An objective alternative is through inverse probability weighting (IPW) of the propensity scores. Although IPW and ANCOVA are asymptotically equivalent, the former may demonstrate inferior performance in finite samples. In this article, we point out that IPW is a special case of the general class of balancing weights, and advocate to use overlap weighting (OW) for covariate adjustment. The OW method has a unique advantage of completely removing chance imbalance when the propensity score is estimated by logistic regression. We show that the OW estimator attains the same semiparametric variance lower bound as the most efficient ANCOVA estimator and the IPW estimator for a continuous outcome, and derive closed-form variance estimators for OW when estimating additive and ratio estimands. Through extensive simulations, we demonstrate OW consistently outperforms IPW in finite samples and improves the efficiency over ANCOVA and augmented IPW when the degree of treatment effect heterogeneity is moderate or when the outcome model is incorrectly specified. We apply the proposed OW estimator to the Best Apnea Interventions for Research (BestAIR) randomized trial to evaluate the effect of continuous positive airway pressure on patient health outcomes. All the discussed propensity score weighting methods are implemented in the R package PSweight.