In mammals, dosage compensation of X linked genes in female cells is achieved by inactivation of one of their two X chromosomes which is randomly chosen. The earliest steps in X-inactivation (XCI), namely the mechanism whereby cells count their X chromosomes and choose between two equivalent X, remain mysterious. Starting from the recent discovery of X chromosome colocalization at the onset of X-inactivation, we propose a Statistical Mechanics model of XCI, which is investigated by computer simulations and checked against experimental data. Our model describes how a 'blocking factor' complex is self-assembled and why only one is formed out of many diffusible molecules, resulting in a spontaneous symmetry breaking (SB) in the binding to two identical chromosomes. These results are used to derive a scenario of biological implications describing all current experimental evidences, e.g., the importance of colocalization.X chromosome inactivation (XCI) is the phenomenon in female mammal early embryo cells by which one of their two X chromosomes, randomly chosen, is transcriptionally silenced, and epigenetically inherited in descendants, to equalize the dosage of X genes products with respect to males [1,2,3]. Crucial aspects of this chromosome-wide stochastic regulatory mechanism, necessary to survival, still elude comprehension despite being the focus of substantial interest for their important scientific and medical implication (see [1,2,3] and Ref.s therein). Starting from the important discovery of X colocalization during XCI establishment [4,5], in this paper we propose a Statistical Mechanics model of the early steps of XCI.Actually, XCI is a multistep process involving [1, 2, 3]: "counting" the number of the X chromosomes of the cell, "choice" of the inactive X, its silencing and maintenance. Silencing and maintenance start being understood: the former is induced by the action of the Xist gene transcript, and maintenance of the inactive state is a paradigm of epigenetic inheritance [3,6]. Counting and choice are, instead, in many respects still mysterious, though it is well established they are controlled by yet unknown sites located within a 1 Mb region on the X, the X-chromosome-inactivation center (Xic), containing several genes and regulators [1,2], such as the Xist gene. We also know that cells having a normal number of autosomes (non sex chromosomes) and extra copies of the X chromosome have only one active X, irrespective of the number of X's [1,2,7].This biological scenario suggests [1, 2, 3] that "controlling factors" for counting and choice derive from autosomes and interact with cis-acting regulatory sequences on the X chromosomes, whose position within the Xic is still unknown. Current models postulate the existence of a "blocking factor" (BF) [1, 2, 3], a complex made of X and autosomal factors, binding to the Xic of just one chromosome per diploid cell preventing its inactivation, as the second unprotected Xic in a female cell is inactivated by default. Multiple factors models were proposed as we...