Yes, it's the actual bedchamber in which the great British statesman was born.
"Of mixed English and American parentage, Churchill was born in Oxfordshire into the wealthy, aristocratic Spencer family. …
He was born on 30 November 1874 at his family's ancestral home, Blenheim Palace in Oxfordshire.
On his father's side, he was a member of the aristocracy as a descendant of John Churchill, 1st Duke of Marlborough.
His father, Lord Randolph Churchill, representing the Conservative Party, had been elected member of parliament (MP) for Woodstock in February 1874. [Wikipedia]