CHIP Stability Act This bill amends title XXI (Children's Health Insurance Program [CHIP]) of the Social Security Act to establish a special rule, with respect to the first quarter of FY2018, for the redistribution of unused CHIP allotments to state child health plans experiencing emergency shortfalls. Specifically, the Centers for Medicare & Medicaid Services (CMS) must redistribute unused allotments to each such state in an amount equal to the state's emergency shortfall before the CMS may redistribute the allotments to any state that is experiencing a nonemergency shortfall.