How much grass is needed to produce a dozen eggs on an 100 acre farm?

None. Chickens don't eat grass, they eat grains, and insects if they can find them. The acreage of the farm they're on is irrelevant. Do you want to rephrase your question?

amez07 disagrees: although chickens don't feed on grass they do contribute to sustainable farming
Yes, they can, if managed correctly. But your question wasn't, "Do chickens contribute to sustainable farming?", it was, "How much grass does it take to produce a dozen eggs?". The answer to that question is "None".

Do you want to ask a different question?

Actually these free range chicken farmers raise what is called "Pasture poultry "and they feed on the grass as well as insects and grain . What the farmer does is put them in movable top only cages so they can feed off the land .The chickens in return fertilize the land they have been on that day.

http://www.lionsgrip.com/pastured.html

These chickens as far as I can tell are raised for slaughter so I can't help with the acreage to egg ratio.

Maybe this book will help
Amazon.com: Pastured Poultry Profits: Joel Salatin: Books (http://www.amazon.com/Pastured-Poultry-Profits-Joel-Salatin/dp/0963810901)