MODERN whales (order Cetacea) are marine mammals that evolved from a land-mammal ancestor, probably a cursorial Palaeocene-Eocene mesonychid(1-3). Living whales are streamlined, lack external hind limbs, and all swim by dorsoventral oscillation of a heavily muscled tail(4,5). A steamlined rigid body minimizes resistance, while thrust is provided by a lunate horizontal fluke attached to the tail at a narrow base or pedicle(6). We describe here a new 46-47-million-year-old archaeocete intermediate between land mammals and later whales. It has short cervical vertebrae, a reduced femur, and the flexible sacrum, robust tail and high neural spines on lumbars and caudals required for dorsoventral oscillation of a heavily muscled tail. This is the oldest fossil whale described from deep-neritic shelf deposits, and it shows that tail swimming evolved early in the history of cetaceans.