We study point-identification and inference methods for local average treatment effects (LATE) when the observed binary treatment may be misclassified. Our setup is nonparametric and allows the individual treatment effect to be heterogeneous across individuals. The misclassification causes an identification bias such that the Wald estimand based on the observables may over- or underestimate LATE. To identify LATE, we correct the bias based on moment restrictions deriving from the use of an additional exogenous variable under plausible conditions. Our identification is constructive so that LATE can be estimated based on the nonlinear generalized method of moments with asymptotically valid inference procedures. Monte Carlo simulations demonstrate the finite sample performance of the proposed method.