A lot of the advice in this thread is good if you want currency that you will actually spend in the country you are visiting, and not change back to dollars. But is this for a short-term rental? Will you be getting the 1000 euros back at the end of the month?

If so, this is what you should do. Get US cash before leaving. Then exchange it upon arrival in Europe, at the airport, with one of the major currency exchange businesses that offer "guaranteed buyback." This means that they will buy back your euros at exactly the rate at which they sold them to you, with no commission. So if you gave them $1500 for your 1000 euros, that's what you get back. No loss on the two-way exchange.

I have done this at American Express at CDG and at Travelex at LHR. AmEx charged nothing for the service; Travelex charged a service fee of a flat 4 pounds. Either way, this is absolutely the way to go if you need a large amount of foreign currency but will be changing it back at the end of your trip.

P.S. I don't doubt that in the history of the world some people who've made cash deposits for vacation rentals have been ripped off. But it's never happened to me, and if the property is listed with a service (as opposed to just Craigslist or something), I wouldn't worry about it.