This paper studies the identifying power of an instrumental variable in the nonparametric heterogeneous treatment effect framework when a binary treatment is mismeasured and endogenous. Using a binary instrumental variable, I characterize the sharp identified set for the local average treatment effect under the exclusion restriction of an instrument and the deterministic monotonicity of the true treatment in the instrument. Even allowing for general measurement error (e.g., the measurement error is endogenous), it is still possible to obtain finite bounds on the local average treatment effect. Notably, the Wald estimand is an upper bound on the local average treatment effect, but it is not the sharp bound in general. I also provide a confidence interval for the local average treatment effect with uniformly asymptotically valid size control. Furthermore, I demonstrate that the identification strategy of this paper offers a new use of repeated measurements for tightening the identified set.