Alderman Ed Burke is sponsoring the proposal.
Tuesday, Burke quoted an article from the Journal of Pediatrics that says the drinks contain high and unregulated amounts of caffeine, and they have serious and adverse side effects in children and teens.
The alderman also quoted government reports on the dangers of energy drinks.
"The number of annual hospital visits connected to highly caffeinated energy drinks doubled from the year 2007 to the year 2011," Burke said.
The makers of energy drinks have maintained their products are safe.
If the ban is approved, Chicago would become the first city in the country to stop the sale of the beverages.