Well, it depends. As with anything that has evolved over one hundred years, it is not always easy to pick one example and call it the first. Most narrow the answer down to two buildings - the Home Insurance Building built in Chicago and the Woolworth Building in New York.
The purist may choose the Home Insurance building. Completed in 1885, it is only ten stories tall. There were several building in Chicago at the time that were taller, but the Home building was the first to employ what is considered the missing link between buildings that were merely tall, and skyscrapers that used the steel frame structure.
The Woolworth Building, finished in 1913, was the first building to use all of the key technologies associated with modern skyscrapers. And at 792 feet, its weight was supported on a foundation built on concrete piers that penetrated the street into solid bedrock below. A sophisticated water tank system provided state-of-the-art plumbing. Architects applied equally sophisticated wind bracing technology and high-speed elevator technology to provide local and express service.