The preferred option for holding an odd-shaped workpiece in a centre lathe is

The correct option is four jaw chuck.

In a centre lathe, different work-holding devices are used depending on the geometry and requirements of the workpiece:
1. Four-Jaw Chuck (Independent Chuck): In this type of chuck, each of the four jaws can be moved and adjusted independently of the others. This independent adjustment allows the chuck to grip asymmetric, irregular, or odd-shaped workpieces (such as square, rectangular, or eccentric parts) securely. It also enables the operator to align and center specific features of the irregular workpiece precisely along the lathe's axis of rotation.
2. Three-Jaw Chuck (Self-Centering Chuck): The jaws in a three-jaw chuck move together simultaneously. While it is highly efficient and automatically centers regular round or hexagonal stock, it is incapable of gripping odd-shaped or irregular workpieces securely.
3. Live and Dead Centres: These centres support long, slender workpieces from both ends to prevent deflection during machining and are not designed for clamping irregular shapes.
4. Lathe Dog: A lathe dog (or carrier) is clamped onto a workpiece to transmit rotational torque from the lathe spindle (via a driving plate) when machining between centres, but it is not a primary chucking device for irregular parts.

Therefore, because its jaws can be positioned at different radial distances to accommodate asymmetry, the four jaw chuck is the preferred option for holding odd-shaped workpieces.