Can you travel by train from Chamonix to Venice?

Where are you looking? I found 3 a day at www.sbb.ch.

It is possible to travel by train from anywhere to anywhere, provided both "anywheres" have a station and are on mainland Europe or are connected by bridge, tunnel or ferry. It is purely a matter of which route and how long.

Look on www.bahn.de
This is showing (for Chamonix-Mont-Blanc to Venezia Santa Lucia) that it will take 8-10 hours and 4 changes.

Indirectly, yes. The easiest way is get to Lyon, train to Milan then transfer to the Venice train.

Steven,
Chamonix to Venice via Lyon is doubling back. Lyon is West of Chamonix, you want to be heading East, via Switzerland. For example:
Chamonix-Mont-Blanc --> Vallorcine (F) --> Martigny --> Brig --> Domodossola --> Milano Centrale --> Venezia S. Lucia

Look it up on www.bahn.de or www.sbb.ch

You cannot easily buy tickets on any single web site, if that's what you're trying to do. Simplest would be to buy them all in Chamonix or an earlier train station, or at least buy the first leg there. www.SBB.ch can sell the portion from Martigny to Milan. The connection from Milan to Venice is sold with advance discounts at www.trenitalia.com.

Thanks to all for your help. My problem was purchasing as everytime I tried buy to tickets on Rail Europe they were unavailable. I will try the two separate web sites suggested. We are traveling with our 9 and 10 year old granddaughters thus I wanted advance tickets to be assured of transportation.

" I tried buy to tickets on Rail Europe"

There's your problem. Rail Europe is a reseller; they do not show all trains; and they often mark up (sometimes substantially) the tickets they do sell. It's best to buy tickets from the website of the country the train originates in; only if you have difficulty should you look at other sites.