A popular option on Euro Commuters. Seen more frequently are partial chain guards - they do a good job at keeping pant legs cleaner. There are also guards that are just a disc on the cranks where the pedals are. That is to keep the chain from coming off to the outside, and also provides minimal trouser protection.
So fully enclosing the chain gives it some of the advantages of a belt drive, because there is no water to wash away the oil the chain stays fairly lubricated. Without dirt, the chain does not need to be cleaned as much, Like with belts, your trousers will not get covered in grease if your leg runs into the chain area. Opening the chain cover can be challenging when fixing a flat or for routine repairs, but overall it is a good system.