Is it possible to withdraw Euros from Swiss ATMs

You can find them (more common in border areas such as Geneva) - but it may end up being a double foreign currency transaction rather than a simple withdrawal. (USD->CHF->EUR). Maybe also hard to avoid at least part of the transaction being at the rate of the ATM. Still your needs might be more important.

You can also try post offices, all but the tiniest ones change CHF into EUR.

Yes, depending where you are. Here in Basel about 1/2 of the machines offer Euros. This is because a large number of Swiss travel across the border regularly, for shopping or whatever, and a lot of the people working in Basel are commuters who live in France or Germany.
This might not be true further from the border, in Bern, Luzern or up in the Alps there would be less demand for Euros, and fewer (If any) machines stocking them.

There is also the question of how much it costs. When I withdraw from one of my own bank's machines, I am charged the "credit card rate" and no commission. If you are not a customer of the bank, they may just charge your bank in Euros (good), or add a surcharge, or go via Franks (double payment).

If all else fails you can convert a small amount of Franks to Euros at the airport before departure, and use the first cash machine after you land. That is assuming this week's Greek banking problems are over by then.

And you had better get ALL the Euros you need BEFORE you arrive in Greece as all of the Greek Banks are now closed because of the Greek debt crisis.

Hi Chris F, thanks for the reply.

We'll be based in Zurich. I'm assuming we'd be able to get Euros there?

gacomeau, I can't give you a definitive answer about Zürich. Whenever I have been there, making a survey of the cash machines has not been on my agenda - sorry!

My guess would be that some would give out Euros, probably less than in here Basel.
Note that when they have Euros, they say on the outside of the machine "CHF/EUR" (or something similar) and you have a choice. They always give out Franks. If all else fails, go to Zürich HB (railway station). All main Swiss railway stations have currency exchange counters which are very competitive.

Or a major bank -- Zurich IS a banking center. Go inside and ask for the foreign exchange desk.

I just used bank cash machines located in the underground mall at the Zurich train station today. A choice of euros or francs was offered.