if it's chainmail or other flexible armor, a hauberk. If it's made of a solid piece of metal, a cuirass or breastplate.
Some cuirasses were made to protect only the chest front, but a lot of them were hinged like a clamshell and protected both front and back. In the Napoleonic Wars notably the Austrian cuirasses only protected their fronts, while the French cuirasses were front and back. In one cavalry battle, the French victory was credited to this fact.