Market microstructure noise is a challenge to high-frequency based estimation of the integrated variance, because the noise accumulates with the sampling frequency. In this paper, we analyze the impact of microstructure noise on the realized range-based variance and propose a bias-correction to the rangestatistic. The new estimator is shown to be consistent for the integrated variance and asymptotically mixed Gaussian under simple forms of microstructure noise, and we can select an optimal partition of the high-frequency data in order to minimize its asymptotic conditional variance. The finite sample properties of our estimator are studied with Monte Carlo simulations and we implement it on high-frequency data from TAQ. We find that a bias-corrected range-statistic often has much smaller confidence intervals than the realized variance.