Among the trees, roebuck and fallow deer still breed and shelter from the gun. Some days you can see perhaps a dozen fallow deer lying in a huddle in the fields, enjoying the warmth. A dangerous habit, particularly this month, when foreign hunters seek trophy heads during the rut.
It is an extraordinarily empty land, which at times seems untouched by modernity. You need a horse to see over the high hedges, and traverse deserted valleys that the few minor roads pass by.
The handful of villages, often owned by a single family, are nestled inconspicuously into hollows. Building sticks to tradition - the flint fronts of the cottages are divided in regular fashion by a couple of lines of bricks or, in the grander churches, by stone. Thatch is making a comeback, complementing the white-washed Dorset "cobb" of some homes.
I'm standing in the midst of the vast woodland, whose depth makes this area so important to naturalists. It is perhaps the closest the countryside comes to an abandoned industrial landscape.
The hazel trees are overgrown - for centuries their straight, flexible branches were conscientiously cropped and bent to build the 3ft-high sheep folds that once spread across the Chase. And the naturally occurring ash and birch were cut to make England's finest brushes. Now it's like a graveyard - peaceful, eerie, but unproductive.
This is an area that has seen many battles. The Civil War devastated Dorset, so evenly was it divided between Royalists and Roundheads. But mostly people have fought over land use. On the edge of the hazel wood is Bloody Shard Gate, scene of a fierce 18th-century skirmish between poachers and gamekeepers. Then there was the 100-year battle by farmers of the Chase for the right to destroy deer that strayed on to their land. In 1829, after 800 years of roaming unmolested, except by the royal hunt, the deer lost their legal protection. In just two days, villagers shot 12,000 of them.
However, the latest battle does not involve poachers or farmers. It is about estate agents seeking to turn this rural idyll into a land with homes fit for the rich - because the Chase is only a 20-minute drive from Salisbury, itself just 90 minutes by train from London. Commuters and week-enders snap up properties.
Later this month, they will learn whether Savills, the upmarket estate agent, has pulled off a coup by persuading the local councils to permit the building of impressive mansions in some of the highest, most conspicuous points of the Chase. The largest is expected to go for pounds 750,000; it is complete with garages, gravel drive, a dovecot and a 42ft-high tiled roof that will tower above the landscape. The plans for 21 luxury homes have caused outrage.
Savills acts as trustee of the Rushmore estate, the family home of Michael Pitt-Rivers, great-grandson of General Pitt-Rivers, who is recognised as a forefather of British archaeology. The estate, once the largest in Dorset, is an "area of outstanding natural beauty", but is desperately short of cash. Mr Pitt-Rivers is ageing and ill.
Much of his wealth has gone on a lifetime of travel, financed by selling the most productive land, leaving his great love, the unproductive woodland of the Chase, as a disproportionate part of the remaining 7,500 acres. Hence, Savills' plan to raise pounds 1.2m for improvements.
In Savills' opinion, the fund-raising measure is vital to save the estate from a sell-off. They warn that a break-up could lead to far more property development. Management of the areas unique natural features would be "nigh on impossible". The best option, they say, is their high-value building, reducing the estate's dependence on farming.
Savills would probably get away with the novel scheme easily, but for the opposition of Edward Bourke, from the neighbouring estate. Mr Bourke, a solicitor, is a typical youngest son of the landed - passed over for the big inheritance, he serves as keeper of family knowledge. Chatting to him, you discover a devoted naturalist, keen to preserve the ancient landscape.
But you also realise that he spearheads a family rivalry that spans nearly 1,000 years. He can date it back to about 1250, when his ancestors were tenants of Mr Pitt-Rivers' antecedents. That went on for 500 years. Then his family came into money, thanks to smuggling, for which the woods of the Chase provided wonderful cover.
They bought their own patch of 1,300 acres bordering the Pitt-Rivers' estate and including the entire village of Chettle. The estate also boasts the elegant Chettle House, designed by Thomas Archer and described by Nikolaus Pevsner as one of the finest examples of baroque architecture in England. A rival, indeed, for the Tudor manor occupied just a few miles away by the much wealthier Pitt-Rivers family.
Fast forward a century or so, to the Thirties. Rushmore is now occupied by George Pitt-Rivers, a famous Fascist in the Thirties, who was interned on the Isle of Man during the Second World War. Mr Bourke tells the tale of a row between George and his great-uncle Edward, in the gunroom at Chettle House.
The story goes that Pitt-Rivers chased Edward through the library, the oak hall, the stone hall, the dining-room and back into the library as he tried to get a good shot. "Fortunately," recalls Mr Bourke, "Pitt- Rivers was tripped up by the butler. The two men never spoke to each other again." And George Pitt-Rivers was never again invited to open the Chettle village fete.
Relations between the latest generation are warmer, but the rivalry has continued. Michael Pitt-Rivers has been as unconventional as his father George. He opposed Fascism and fought in the Second World War. However, he was, like his father, also jailed, but for a different reason: for indecency involving an under-age boy, in the Fifties.
In almost every detail, Michael rejected his father, who had taken his heterosexuality very seriously, marrying four times. Michael was married to, and then divorced, George Orwell's widow, an alliance that must have irritated his father's fascist principles. But he has since spent most of his adult life with his companion, William Davis.
When Michael was released from prison, the Bourkes invited him to to open the Chettle village fete. "My mother," recalls Mr Bourke, "used to say, 'who would we rather have to open the fete - a wife-beater like George or a homosexual?' She much preferred a homosexual."
Nevertheless, the Bourkes have looked on somewhat disapprovingly as Pitt-Rivers squandered his inheritance. Meanwhile, they have toiled away at their 1,300 acres, which, despite the fine house, is a vegetable patch compared with the Pitt-Rivers' estate. They are in no mood to give him the easy way out and let his trustees cash in on a money-making loophole in the law.
"It would," says Mr Bourke, "create a completely unacceptable precedent if estate owners were able to secure planning permission for dwellings in the open countryside in order to provide money to maintain and enhance their estates."
This, then, is a story of a battle to save the countryside from the rush to build in green fields. A typical modern tale.
It is also about the decline of a great estate, which once spanned 35,000 acres, and whose owner was lord of the Chase. But, as in all country tiffs, it is crucially about long memories and hidden rivalries. We should find out soon who triumphs in this latest round between two ancient Dorset families.