We propose a new approach for efficient estimation of heterogeneous treatment effects in difference-in-differences (DiD) settings in the presence of arbitrary serial correlation and time-varying variances in the idiosyncratic errors. Using the standard conditional parallel trends and no anticipation assumptions, and a representation of treatment effects as parameters in a linear projection, we demonstrate that treatment effects are identified using generalized least squares (GLS) with an unrestricted variance-covariance matrix. The new estimator is consistent and asymptotically efficient under a system homoskedasticity assumption. Through simulations, we show that across all scenarios the new Feasible GLS estimator is as efficient as competing estimators that allow staggered interventions, including Wooldridge's extended two-way fixed effects, the Callaway and Sant’Anna estimator, and De Chaisemartin and D’Haultfoeuille estimator. Moreover, Feasible GLS offers significant efficiency gains (>30%) when serial correlation or time heteroskedasticity are nontrivial. We also show how the methodology extends to staggered DiD settings where some units may exit treatment.