from Wikipedia, so read it with a grain of salt:

Earliest uses

Slate's Daniel Engber dates the modern usage to 1974 college campuses, where it was perhaps an outgrowth of the Vietnam War.^[5]

The origins of the phrase are uncertain, with some speculating that it may refer to being "out in the open" or "ready for action." According to Engber many soldiers do go without underwear to "increase ventilation and reduce moisture." The earliest known use of the term in print is January 22, 1985 when Jim Spencer wrote in the Chicago Tribune:

<blockquote>

"Furthermore, colored briefs are 'sleazy' and going without underwear ('going commando', as they say on campus) is simply gross".

</blockquote>

The origin of the term "going commando" may connect to the tradition in military units of Scottish heritage to not wear underwear under their kilts. The first Commando units were raised and trained in World War II in Scotland (which is where the present-day Commando Monument is). It is said that Scottish soldiers once used the expression "regimental," to describe the state of wearing no shorts under a kilt; allegedly, Scottish drill instructors carried a long stick with a mirror on the end to verify that soldiers were properly regimental.^{[citation needed]}

In the British Forces, the term 'going commando' actually refers to not washing and generally being dirty, as Royal Marine Commandos and other elite regiments tend to have a reputation of doing when on exercise, or on patrol.^{[citation needed]}