PAONIA, Colo. — This is a story of a quiet billionaire and a middle-class mountain town, of class divisions, small-town quarrels and competing visions of the future of the West. But at its core, like so many stories here in the aspen-dappled hillsides, it is really all about land.

Specifically, it is about a belt of public land that cuts straight through a ranch owned by the industrialist Bill Koch, whose brothers Charles and David are top contributors to conservative Republican causes.

A century ago, sheepherders used the corridor to drive their flocks from valley floors to high grazing grounds without crossing private property. For decades after, it was mostly forgotten by everyone but a few hunters and hikers — one of dozens of such access strips that stipple maps of the West like a shower of hyphens.

But recently, Mr. Koch has made it perhaps the most contested ground for miles around, setting off a debate about private property and public access, privilege and tradition in an era when boutique ranches and sprawling new Western manors are brushing up against working-class rural communities.