It varies widely. You best bet would be to ask someone at your institution. Some universities provide a set stipend in addition to salary for the chair, others pay the chair on a 10, 11, or 12 month basis instead of 9 month, and some new chairs negotiate a higher base salary. Given the current budget, my institution last week made some poor humanities professor take on chairing not one, but two departments, with NO salary increase and only a single course load reduction.
How can an institution "make" some one chair a department. Why wouldn't this professor offer a hearty "f**k you" to the evil b@stards who would ask someone to do this on a 9 month salary? Did this prof say "sure, but I ain't doin' a lick of admin work in June, July, and August"? This is really sick.
And yes, asking for at least a 10 month contract makes sense. But ask for 12, and see what happens. And if they don't offer it, you might want to say no. There's no point giving yourself this headache without a bit of additional pay.