Early in the development of female mammals, one of the two X chromosomes is silenced in half of cells and the other X chromosome is silenced in the remaining half. The basis of this apparent randomness is not understood. We show that before X-inactivation, the two X chromosomes appear to exist in distinct states that correspond to their fates as the active and inactive X chromosomes. Xist and Tsix, noncoding RNAs that control X chromosome fates upon X-inactivation, also determine the states of the X chromosomes prior to X-inactivation. In wild-type ES cells, X chromosomes switch between states; among the progeny of a single cell, a given X chromosome exhibits each state with equal frequency. We propose a model in which the concerted switching of homologous X chromosomes between mutually exclusive future active and future inactive states provides the basis for the apparently random silencing of one X chromosome in female cells.