The Desk on a chest was popular during the Renaissance and to some extent during the Middle Ages, in much of Europe. It was also used by officers as a form of Campaign desk during much of the 18th and 19th centuries.
When the top and bottom chests are permanently attached or built as one piece we have a desk form called a Fall front desk. It is supposed that the Fall front desk form gradually evolved from the Desk on a chest towards the end of the Renaissance.
See also the list of desk forms and types.