In order to enter, Google is asking people to say on Twitter and Google+ how they would use the glasses if they were given a set.
Google is asking entrants to tag their ideas, which must be no longer than 50 words, with the hashtag #ifIhadglass. Entrants are also allowed to use up to five photos and a video up to 15 seconds in length.
Applications must be made before 27 February and Google will award the glasses to the lucky competition winners at a pick-up experience in New York, San Francisco or Los Angeles.
The competition is open anyone over the age of 18 living in the US and will give them the opportunity to try out the glasses before they go on general sale. While Google hasn't set a date when that will be, it's thought Google Glass could reach general availability at the end of 2014.
However, there's no such thing as a free lunch for would-be Glass owners: competition winners will still need to spend $1,500 to get their Explorer Edition of the glasses.
To coincide with the competition launch, Google released a new YouTube video demonstrating the headset's initial features, user interface and the overall experience of using the device.
The video shows Google Glass in action and suggests that users will be able to take photos and record what they see by giving voice commands like "OK Glass, take a picture" or "OK Glass, record a video". The video also shows features such as voice-controlled searches and Google+ Hangouts.