A Desk on a chest is an antique Portable desk

Portable desk

The portable desk has not one but many forms. In a sense, the portable desk is a long-lost ancestor of the portable computer, and the modern laptop could be considered an atavistic grandchild of the 19th-century Lap desk....

 made up of two chests, the bottom one usually having drawers and the top one having a hinged desk

Desk

A desk is a furniture form and a class of table often used in a work or office setting for reading or writing on or using a computer. Desks often have one or more drawers to store office supplies and papers. Unlike a regular table, usually only one side of a desk is suitable to sit on . Not all...

 surface which also serves as a side mounted lid. A Vargueno or Bargueno desk

Bargueno desk

The Bargueño is a desk first produced in the 15th century that continues to be produced to this day. The only other style of desk which is known to have been continuously produced for so long is the trestle desk, but some authorities exclude this desk from consideration because in early times it...

 is a specific form of the "Desk on a chest" when it is mounted on a chest of drawers called a "Taquillon".

The "Desk on a chest" was popular during the Renaissance

Renaissance

The Renaissance was a cultural movement that spanned roughly the 14th to the 17th century, beginning in Italy in the Late Middle Ages and later spreading to the rest of Europe. The term is also used more loosely to refer to the historical era, but since the changes of the Renaissance were not...

 and to some extent during the Middle Ages

Middle Ages

The Middle Ages is a periodization of European history from the 5th century to the 15th century. The Middle Ages follows the fall of the Western Roman Empire in 476 and precedes the Early Modern Era. It is the middle period of a three-period division of Western history: Classic, Medieval and Modern...

, in much of Europe

Europe

Europe is, by convention, one of the world's seven continents. Comprising the westernmost peninsula of Eurasia, Europe is generally 'divided' from Asia to its east by the watershed divides of the Ural and Caucasus Mountains, the Ural River, the Caspian and Black Seas, and the waterways connecting...

. It was also used by officers as a form of Campaign desk

Campaign desk

A campaign desk is an antique desk of normal size which was used by officers and their staffs in rear areas during a military campaign.The campaign desk was usually the private property of the officer, as was his uniform and other military implements. It was in general handcrafted by a master...

 during much of the 18th and 19th centuries.

When the top and bottom chests are permanently attached or built as one piece there is a desk form called a Fall front desk

Fall front desk

The fall front desk can be considered the cousin of the Secretary desk. Both have a main working surface or desktop which does double duty as a cover to seal up papers and other items located in small shelves or small drawers placed one on top of the other in front of the user...

. 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.