A Chai blend, just like any other tea blend, won’t really go “bad”, but it can get stale.  Chai tea blends can stay fresh for up to a year if you always store it in a cool, dark place keeping it away from heat, light, oxygen and moisture.  Never store tea in the fridge.  Tea will last longer if stored in an opaque, airtight container away from items that can leach their flavour into the tea.