Purpose: To construct a simple intraday estimator of the variance of an asset that is robust to price contamination (such as market microstructure noise) and achieves the classical rate of convergence (root-T). Originality: Current intraday variance estimators that are robust to price contamination are computationally expensive to calculate, occasionally infeasible, and at best only converge in the fourth root of T. The originality of our work is to improve on each of these points. Key literature / theoretical perspective: Two key papers are: Ait-Sahalia, Mykland, Zhang (2011) “Ultra High-Frequency Volatility Estimation With Dependent Microstructure Noise”; Barndorff-Nielsen, Hansen, Lunde, Shephard (2008) “Designing Realized Kernels to Measure the ex post Variation of Equity Prices in the Presence of Noise”. Design/methodology/approach: We derive a maximum likelihood estimator by utilizing observable bounds of the latent price process. Findings: For large true variance of the latent process relative to the distance between the observable upper and lower bound, the maximum likelihood estimator performs almost as well as the (infeasible) best possible estimator. For smaller true variances, the maximum likelihood estimator admits a negative bias that strengthens as true variance (for fixed bound width) decreases. Research limitations/implications: The research provides an alternative methodology to the nonparametric approaches to volatility estimation that are currently popular. Practical and Social implications: Improving estimation of asset variance is important in many areas of Finance, particularly portfolio management, and risk analysis.