Female mammalian cells achieve dosage compensation of X-encoded genes by X chromosome inactivation (XCI). This process is thought to involve X chromosome counting and choice. To explore how this process is initiated, we analyzed XCI in tetraploid XXXX, XXXY, and XXYY embryonic stem cells and found that every X chromosome within a single nucleus has an independent probability to initiate XCI. This finding suggests a stochastic mechanism directing XCI counting and choice. The probability is directly proportional to the X chromosome:ploidy ratio, indicating the presence of an X-encoded activator of XCI, that itself is inactivated by the XCI process. Deletion of a region including Xist, Tsix, and Xite still results in XCI on the remaining wild-type X chromosome in female cells. This result supports a stochastic model in which each X chromosome in a nucleus initiates XCI independently and positions an X-encoded trans-acting XCI-activator outside the deleted region.