(GMT)07 JUL 2016 WALSLO1:
There are many operators who provide airport transfer service from Geneva to Chamonix. Vans and mini buses are most popular option.
There were bunch of websites but it took quite a while for me to find how long it takes. See the below journey time.
1hr 10 mins to 1 hr 30 mins between Geneva and Chamonix
1hr to 1 hr 30 mins between Geneva and Les Houches / Servoz
1hr 30 mins to 1 hr 45 mins between Geneva and Argentiere