According to that 5970s use 304W under maximum load. x2 is 608W. Then you have to add the rest of the system to that to know what your likely maximum power consumption will be.
But you definitely won't be overloading a 1000W PSU. The only question remains whether you feel comfortable stressing your PSU to the level that you will be doing.
If it is a high quality unit then you shouldn't necessarily be uncomfortable because a high quality unit can deliver its stated wattage all day.
Of course it depends on the PSU, do you already have it? If so what is the model name? If not then what is your budget and where are you buying from?
Do you have a budget for the case?
Listing some of your preferences for a case (besides fitting 5970s and other obvious things like 'good airflow') would be helpful in choosing some to recommend.
For a system using two Radeon HD 5970 graphics cards in 2-way CrossFireX mode a minimum of an 850 Watt or greater power supply that has a combined +12 Volt continuous current rating of 70 Amps or greater and that has at least two 6-pin and two 8-pin PCI-Express supplementary power connectors is recommended.
It's not the wattage of the power supply that you should be looking at. The only critical power supply specification is the power supply unit's combined +12 Volt continuous current rating. Just make sure its combined +12 Volt continuous current rating is 70 Amps or greater and you'll have enough.
A decent 1000 Watt power supply will have a combined +12 Volt continuous current rating of at least 80 Amps.
I wouldn't let a single 5970 near any of those units except the higher wattage Silent Pro Gold units, most of cooler masters other units are moderate to extremely crappy. You are talking about powering two very expensive cards, get a good PSU, it will last about twice as long as those cards will.
The problems I've been reading about that psu is that it gets very noisy and the cables are not long enough for a full tower case and/or a case with a bottom mounted psu. The price is pretty good though so I'll have to do a little more searching to see if it's worth it.