In some cells pairing of homologous chromosomes happens at particular moments during the cell life cycle. A Statistical Mechanics model based on some experimental data is presented and discussed here for this phenomenon. Under this model, chromosomes pair at special regions whose interaction is mediated by some molecules which diffuse in cells' nuclei and can bind them. Concentration of these molecules acts as a switch for pairing: at low concentrations chromosomes move independently one from another whereas if concentration is above a certain threshold value, chromosomes colocalize. Monte Carlo simulations of this model have been performed to test its eficiency and the effect on pairing levels of chromosomal binding sites deletions.