We introduce a novel estimator of the quadratic variation that is based on the the- ory of Markov chains. The estimator is motivated by some general results concerning …ltering contaminated semimartingales. Speci…cally, we show that …ltering can in prin- ciple remove the eects of market microstructure noise in a general framework where little is assumed about the noise. For the practical implementation, we adopt the dis- crete Markov chain model that is well suited for the analysis of …nancial high-frequency prices. The Markov chain framework facilitates simple expressions and elegant analyti- cal results. The proposed estimator is consistent with a Gaussian limit distribution and we study its properties in simulations and an empirical application.