We are planning a trip to Chamonix next winter. I was wondering if it is possible to rent a car there with an American drivers license. Also, is it recommended to buy local insurance or just use my Geico policy that I have for my truck here?
A US license will be fine, especially at any airport hire location (I imagine you plan on landing at Geneva?)
Hire cars in Europe normally come with insurance included, although there is also typically a ~€1000 excess for damage to the vehicle, which you can pay an additional (typically vastly overpriced) fee to reduce. I'd be suprised if your US car insurance will cover you to drive another vehicle on a different continent without paying a suppliment at the very least.
It's not necessary to hire a car though if you are planning on staying in Chamonix. There are a variety of reasonably priced transfer options from Geneva airport (typically jump in a minibus with others, be dropped off at your place of stay) - just search for "Chamonix Transfers". Chamonix town itself is quite small (easily walkable), and there's a train that operates up and down the valley, as well as a selection of bus services for skiiers. If you're staying in a more remote chalet, or want to travel to less likley areas, then a car obviously adds value.
I'll give the answer the other way: as a Belgian who rent cars in USA, prior to coming to USA, I went to my local administration and ordered an international driving license. It is basically a holiday card size 12 pages booklet containing the translation of all my local driving license fields into 4 languages. It has my name and other information on it, has a stamp from my local administration, and is only valid if shown with my local driving license. I did rent cars in New York, in North Carolina and in California without any problem, but I have not been pulled over by police, so I can't really tell what they would do. That's supposed to be legal anyway. I would however strongly suggest reading Wikipedia page about driving in "the country where you will go", because for example, the American rule "right turn on red light" is forbidden everywhere except in USA. There are other regulations that might be totally obvious to Europeans, but would seem weird to someone coming from abroad.