How To Ski
Chamonix Switzerland And Italy
All In ONe day

I'm assuming your question is whether you could ski in Chamonix then ski directly into another resort in Italy as well as in Switzerland much like you'd do in Zermatt and Cervinia.

In Zermatt, Switzerland you'd go up to the top of the Plateau Rosa, then downhill into the groomed slopes of Cervinia in Italy. So, it's one resort directly to another resort.  The ridge happens to be the border between the countries as well as the boundary for the two resorts.

It's not quite so simple in Chamonix, Steve. The resorts here are not back to back requiring off-piste, back country skiing.

Off Piste Italy To Chamonix

While Courmayeur, Italy is on the southern side of the Alps from Chamonix there's no direct winter access via lifts or cable cars, but skiers do access Chamonix from the Italian lifts into the Vallee Blanche, France for off-piste skiing.  It generally takes half a day for this excursion, but expert skiers familiar with the territory can head down the Vallee Blanche in a couple of hours.

Off Piste Chamonix Switzerland

Google Map with locations of (A) Trient Switzerland, (B) Vallorcine and (C) Chamonix

Chamonix is closest to the border with Switzerland at Vallorince / Le Tour and you can access Trient in Switzerland via a steep back country route. Again this is off-piste and there are the attendant dangers of avalanches. Please take a guide with you as back country means crevasses, cliffs, seracs let alone avalanches. Head for the Domaine de Balme and go to the top of the Autannes lift, then hike up the steep ascent to the Col de Balme, on the border with Switzerland.  Snow shoes and crampons are a must on the hike to the ridge.  We are talking here couloirs. You'll find details on the offpiste route to Switzerland in the book "Mont Blanc Ski Tours". It's in both French and English.

Click Here To Buy Mont-Blanc Ski Tours

Check the return bus times from Trient, Switzerland to Vallorcine, France where you get onto the train back to town.  This excursion through Switzerland would usually take half a day and an early start is recommended.

Google Map : Route From (A) Courmayeur to (C) Verbier, Switzerland

On-Piste 3 Countries On One Pass In One Day

If you wanted to downhill in all the three sister resorts on the one Chamonix pass, it's not impossible.  You'd have to start early, have access to a car and a driver who looks is happy to be your support person. 

I'd suggest starting at Courmayeur and being there when lifts first open. Don't catch the free bus from Chamonix  - it starts too late if you're wanting to "do" Verbier as well on the same day. Explore here till say 11 am then head off to Switzerland.  The drive takes about 2 hours and let your driver hassle around with parking which is a minor nightmare at this beautiful but town planning challenged resort.

You'll then have a good 3 hours at Verbier before lifts close. You may encounter some ticket counter staff unaccustomed to the co-ticketing with Chamonix and this may take time while they seek clarification with their manager, so allow time for that.

So, yes you can ski 3 countries in one day - France at Chamonix Switzerland and Italy but it takes a little effort.

Enjoy your vacation, Steve!