Life on a Cattle Ranch has a great post describing how cattle are raised sustainably on native North American prairies in the Flint Hills of Kansas. A strategy of prescribed burns and field rotation allows the ranchers to turn grass into meat year after year without chemical inputs.
The reason this system works out so well is that this ecosystem is already adapted to the pressures of regular wildfires and heavy grazing - by bison! The bison are pretty much all gone, but the cattle are a pretty good functional ecological replacement.
There aren't many situations where resources can be extracted from the land this intensively with this little impact, but it's great when it works.
The picture, by the way, is of some bison on the Konza Prairie, a famous nature preserve/experimental research station in the Flint Hills. It's part of an ambitious ecology research system known as the LTER (Long Term Ecological Research Network) that endeavors to discover fundamental ecology operating at large spatiotemporal scales.